Stress management in composite biopolymer networks

Living tissues show an extraordinary adaptiveness to strain, which is crucial for their proper biological functioning. The physical origin of this mechanical behaviour has been widely investigated using reconstituted networks of collagen fibres, the principal load-bearing component of tissues. However, collagen fibres in tissues are embedded in a soft hydrated polysaccharide matrix which generates substantial internal stresses whose effect on tissue mechanics is unknown. Here, by combining mechanical measurements and computer simulations, we show that networks composed of collagen fibres and a hyaluronan matrix exhibit synergistic mechanics characterized by an enhanced stiffness and delayed strain-stiffening. We demonstrate that the polysaccharide matrix has a dual effect on the composite response involving both internal stress and elastic reinforcement. Our findings elucidate how tissues can tune their strain-sensitivity over a wide range and provide a novel design principle for synthetic materials with programmable mechanical properties

Characterization of the microstructural properties that are predictive of regain in strength in phosphate-deficient mice

Fracture healing occurs in a discrete set of steps, which recapitulates embryonic endochondral bone formation. Pathophysiologies of the fracture healing that prolong the fracture repair or result in non-union may be associated with either environmental or congenital deficiencies. Phosphate deficiency resulting from either dietary or genetic perturbations can impede proper fracture healing and if prolonged can result in delayed union. The clinical assessment of regain of mechanical function is determined by measuring weight-bearing ability, palpation and various radiological approaches. These methods in general only provide qualitative evidence but are lacking in quantitative evidence of the regain in mechanical strength. The aim of this study was to characterize the microstructural properties obtained by micro-computed tomography of fracture calluses at various stages of healing and develop correlations between these structural parameters and mechanical properties that define regain of function. Transverse, mid-diaphyseal fractures were produced on the right leg in three different murine genetic strains—A/J (AJ), C57BL/6J (B6), and C3H/HeJ (C3). Each mouse was either fed a control or phosphate deficient diet that produces a hypophosphatemic state and generates an environmental state that impairs fracture healing. Those on a phosphate deficient diet were kept on this diet for 14 days post-fracture. Fractured limbs were studied at four different post-operative time points—14, 21, 35, and 42. These four time points were based on callus stability and various phases in callus development. Contralateral limbs served as a control, representing full regain of strength. Day 0 contralateral limbs were used for the control group. Contralateral limbs were imaged and torsion tested for each strain on both control and phosphate-deficient diets. The data reveals that in regards to bone volume fraction, bone mineral density, and tissue mineral density all three strains show a progressive return to non-fractured, control values but even by post-operative day 42 do not show a 100% regain in microstructural properties. While there are interactions between specific post-operative time points and the dietary restriction, by post-operative day 42 microstructural properties showed no significant differences between the two groups, suggesting that the effects of phosphate deficiency are reversible upon a return to normal dietary conditions. The AJ and B6 strains show significant interaction between post-operative time point and dietary restrictions earlier in the fracture repair process (post-operative days 14 and 21), whereas the C3 mice show these interactions at later time points, at post-operative 35 and 42 days. Phosphate deficiency induces an overshoot in mechanical properties at post-operative day 21 for AJ and B6 strains and at post-operative day 35 for the C3 strain that appears to be part of a process in which maximum torque and work to failure undergo a compensatory phase in which these two mechanical properties are significantly higher than in non-fractured, control limbs. The overshoot in maximum torque and work to failure is part of an adaptive process in which the callus first overshoots and subsequently returns to non-fractured control values. These results suggest that while microstructural properties and mechanical properties are often affected by diet, this is a reversible phenomenon, which holds implications for those with phosphate deficiency due to either a metabolic or dietary disorder. If normal phosphate intake and absorption are achieved by the period at which couple remodeling in initiated (14 post-fracture) the effects on microstructural and weight bearing levels are reversible. The slower healing seen in C3 mice evidenced by the later regain in microstructural and mechanical integrity may provide a model for patients whose fractures show delayed healing in the clinic. The microstructural properties discussed have the potential to play a role in the clinic to assess fracture healing. With the advent of greater resolution CT imaging assessing these microstructural properties can be useful in determining the progression of healing

Cell organization in soft media due to active mechanosensing

Adhering cells actively probe the mechanical properties of their environment and use the resulting information to position and orient themselves. We show that a large body of experimental observations can be consistently explained from one unifying principle, namely that cells strengthen contacts and cytoskeleton in the direction of large effective stiffness. Using linear elasticity theory to model the extracellular environment, we calculate optimal cell organization for several situations of interest and find excellent agreement with experiments for fibroblasts, both on elastic substrates and in collagen gels: cells orient in the direction of external tensile strain, they orient parallel and normal to free and clamped surfaces, respectively, and they interact elastically to form strings. Our method can be applied for rational design of tissue equivalents. Moreover our results indicate that the concept of contact guidance has to be reevaluated. We also suggest that cell-matrix contacts are upregulated by large effective stiffness in the environment because in this way, build-up of force is more efficient.Comment: Revtex, 7 pages, 4 Postscript files include

Wrinkling of microcapsules in shear flow

Elastic capsules can exhibit short wavelength wrinkling in external shear flow. We analyse this instability of the capsule shape and use the length scale separation between the capsule radius and the wrinkling wavelength to derive analytical results both for the threshold value of the shear rate and for the critical wave-length of the wrinkling. These results can be used to deduce elastic parameters from experiments.Comment: 4 pages, 2 figures, submitted to PR

Collective effects in cellular structure formation mediated by compliant environments: a Monte Carlo study

Compliant environments can mediate interactions between mechanically active cells like fibroblasts. Starting with a phenomenological model for the behaviour of single cells, we use extensive Monte Carlo simulations to predict non-trivial structure formation for cell communities on soft elastic substrates as a function of elastic moduli, cell density, noise and cell position geometry. In general, we find a disordered structure as well as ordered string-like and ring-like structures. The transition between ordered and disordered structures is controlled both by cell density and noise level, while the transition between string- and ring-like ordered structures is controlled by the Poisson ratio. Similar effects are observed in three dimensions. Our results suggest that in regard to elastic effects, healthy connective tissue usually is in a macroscopically disordered state, but can be switched to a macroscopically ordered state by appropriate parameter variations, in a way that is reminiscent of wound contraction or diseased states like contracture.Comment: 45 pages, 7 postscript figures included, revised version accepted for publication in Acta Biomateriali

Controlling cell-matrix traction forces by extracellular geometry

We present a minimal continuum model of strongly adhering cells as active contractile isotropic media and use the model to study the effect of the geometry of the adhesion patch in controlling the spatial distribution of traction and cellular stresses. Activity is introduced as a contractile, hence negative, spatially homogeneous contribution to the pressure. The model shows that patterning of adhesion regions can be used to control traction stress distribution and yields several results consistent with experimental observations. Specifically, the cell spread area is found to increase with substrate stiffness and an analytic expression for the dependence is obtained for circular cells. The correlation between the magnitude of traction stresses and cell boundary curvature is also demonstrated and analyzed.Comment: 12 pages, 4 figure