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

Focal adhesions as mechanosensors: the two-spring model

Adhesion-dependent cells actively sense the mechanical properties of their environment through mechanotransductory processes at focal adhesions, which are integrin-based contacts connecting the extracellular matrix to the cytoskeleton. Here we present first steps towards a quantitative understanding of focal adhesions as mechanosensors. It has been shown experimentally that high levels of force are related to growth of and signaling at focal adhesions. In particular, activation of the small GTPase Rho through focal adhesions leads to the formation of stress fibers. Here we discuss one way in which force might regulate the internal state of focal adhesions, namely by modulating the internal rupture dynamics of focal adhesions. A simple two-spring model shows that the stiffer the environment, the more efficient cellular force is built up at focal adhesions by molecular motors interacting with the actin filaments.Comment: Latex, 17 pages, 5 postscript figures include

Planar sandwich antennas for submillimeter applications

A planar receiving antenna with a predictable pattern at submillimeter wavelength is demonstrated experimentally for the first time. It is single lobed and efficient, with a gain of approximately 8 dB at a wavelength of 119 µm

Inventory Management under Product Mis-identification/Shipment Errors

“Wrong-product” delivery - the delivery of a product different from that desired - is a significant, but as yet unexplored problem in supply-chain management research. There are basically two reasons for wrong-product delivery: either the wrong product is mistakenly ordered or the right product is ordered but the wrong product is picked/shipped. This paper defines and analyzes the “wrong-product delivery” problem using a 2-product newsvendor model. Two non-substitutable products may be ordered at the beginning of each time period. However, whenever product i is ordered, then with known probability i, product j is delivered; i, j = 1, 2(i 6= j). First, we analyze the “no-recourse scenario”, where management correctly stores whatever was received, but takes no other action. We establish the form of the optimal policy and conduct sensitivity analysis. Although our modeling framework is simple, our results are unexpected and non-intuitive. For example, it is well known that in the single-product newsvendor model, increasing the uncertainty of demand or supply will yield an increase in the corresponding target basestocks and safety stocks. However, increasing the risk of a wrong-product error yields a decrease in the corresponding basestocks and safety stocks. Further, although target basestocks in the single-product newsvendor model are invariant to increases in on-hand inventory, we show that the target basestock for either product is non-decreasing as its inventory increases. We also demonstrate that the cost impact of wrong-product uncertainty is comparable, if not larger than, the cost impact of demand uncertainty. Next, we analyze the “recourse scenario” where management is able to correct errors but only by incurring a fixed cost of $K. We show that it is optimal to take recourse when the wrong-product uncertainty is sufficiently small, but not take recourse when the wrong-product uncertainty is high. In strategic terms, our analysis provides insight into the cost impact of wrong-product errors, and, hence, the importance of reducing them.Supply chain management, Inventory management, Shipment errors, Ordering errors, Yield management, Unreliable supply

Mean encounter times for cell adhesion in hydrodynamic flow: analytical progress by dimensional reduction

For a cell moving in hydrodynamic flow above a wall, translational and rotational degrees of freedom are coupled by the Stokes equation. In addition, there is a close coupling of convection and diffusion due to the position-dependent mobility. These couplings render calculation of the mean encounter time between cell surface receptors and ligands on the substrate very difficult. Here we show for a two-dimensional model system how analytical progress can be achieved by treating motion in the vertical direction by an effective reaction term in the mean first passage time equation for the rotational degree of freedom. The strength of this reaction term can either be estimated from equilibrium considerations or used as a fit parameter. Our analytical results are confirmed by computer simulations and allow to assess the relative roles of convection and diffusion for different scaling regimes of interest.Comment: Reftex, postscript figures include

Effect of adhesion geometry and rigidity on cellular force distributions

The behaviour and fate of tissue cells is controlled by the rigidity and geometry of their adhesive environment, possibly through forces localized to sites of adhesion. We introduce a mechanical model that predicts cellular force distributions for cells adhering to adhesive patterns with different geometries and rigidities. For continuous adhesion along a closed contour, forces are predicted to be localized to the corners. For discrete sites of adhesion, the model predicts the forces to be mainly determined by the lateral pull of the cell contour. With increasing distance between two neighboring sites of adhesion, the adhesion force increases because cell shape results in steeper pulling directions. Softer substrates result in smaller forces. Our predictions agree well with experimental force patterns measured on pillar assays.Comment: 4 pages, Revtex with 4 figure

Stochastic simulations of cargo transport by processive molecular motors

We use stochastic computer simulations to study the transport of a spherical cargo particle along a microtubule-like track on a planar substrate by several kinesin-like processive motors. Our newly developed adhesive motor dynamics algorithm combines the numerical integration of a Langevin equation for the motion of a sphere with kinetic rules for the molecular motors. The Langevin part includes diffusive motion, the action of the pulling motors, and hydrodynamic interactions between sphere and wall. The kinetic rules for the motors include binding to and unbinding from the filament as well as active motor steps. We find that the simulated mean transport length increases exponentially with the number of bound motors, in good agreement with earlier results. The number of motors in binding range to the motor track fluctuates in time with a Poissonian distribution, both for springs and cables being used as models for the linker mechanics. Cooperativity in the sense of equal load sharing only occurs for high values for viscosity and attachment time.Comment: 40 pages, Revtex with 13 figures, to appear in Journal of Chemical Physic