Cellular signaling beyond the Wiener-Kolmogorov limit

Accurate propagation of signals through stochastic biochemical networks involves significant expenditure of cellular resources. The same is true for regulatory mechanisms that suppress fluctuations in biomolecular populations. Wiener-Kolmogorov (WK) optimal noise filter theory, originally developed for engineering problems, has recently emerged as a valuable tool to estimate the maximum performance achievable in such biological systems for a given metabolic cost. However, WK theory has one assumption that potentially limits its applicability: it relies on a linear, continuum description of the reaction dynamics. Despite this, up to now no explicit test of the theory in nonlinear signaling systems with discrete molecular populations has ever seen performance beyond the WK bound. Here we report the first direct evidence the bound being broken. To accomplish this, we develop a theoretical framework for multi-level signaling cascades, including the possibility of feedback interactions between input and output. In the absence of feedback, we introduce an analytical approach that allows us to calculate exact moments of the stationary distribution for a nonlinear system. With feedback, we rely on numerical solutions of the system's master equation. The results show WK violations in two common network motifs: a two-level signaling cascade and a negative feedback loop. However the magnitude of the violation is biologically negligible, particularly in the parameter regime where signaling is most effective. The results demonstrate that while WK theory does not provide strict bounds, its predictions for performance limits are excellent approximations, even for nonlinear systems.

Characterization of polystyrene under shear deformation using Molecular Dynamics

Nano-filled polymers are becoming more and more important to meet the continuously growing requirements of modern engineering problems. The investigation of these composite materials at the molecular level, however, is either prohibitively expensive or just impossible. Multiscale approaches offer an elegant way to analyze such nanocomposites by significantly reducing computational costs compared to fully molecular simulations.When coupling different time and length scales, however, it is in particular important to ensure that the same material description is applied at each level of resolution.The Capriccio method, for instance, couples a particle domain modeled with molecular dynamics (MD) with a finite element based continuum description and has been used i.a. to investigate the effects of nano-sized silica additives embedded in atactic polystyrene (PS). However, a simple hyperelastic constitutive law is used so far for the continuum description which is not capable to fully match the behavior of the particle domain. To overcome this issue and to enable further optimization of the coupling scheme, the material model used for the continuum should be derived directly from pure MD simulations under thermodynamic conditions identical to those used by the Capriccio method.To this end, we analyze the material response of pure PS under uniaxial deformation using strain-controlled MD simulations. Analogously, we perform simulations under pure shear deformation to obtain a comprehensive understanding of the material behavior.As a result, the present PS shows viscoelastic characteristics for small strains, whereas viscoplasticity is observed for larger deformations. The insights gained and data generated are used to select a suitable material model whose parameters have to be identified in a subsequent parameter optimization.

The role of mechanical interactions in EMT

The detachment of cells from the boundary of an epithelial tissue and the subsequent invasion of these cells into surrounding tissues is important for cancer development and wound healing, and is strongly associated with the epithelial-mesenchymal transition (EMT). Chemical signals, such as TGF-beta, produced by surrounding tissue can be uptaken by cells and induce EMT. In this work, we present a novel cell-based discrete mathematical model of mechanical cellular relaxation, cell proliferation, and cell detachment driven by chemically-dependent EMT in an epithelial tissue. A continuum description of the model is then derived in the form of a novel nonlinear free boundary problem. Using the discrete and continuum models we explore how the coupling of chemical transport and mechanical interactions influences EMT, and postulate how this could be used to help control EMT in pathological situations.

Stress and strain effects

This chapter extends this book’s discussion of bandstructure, band discontinuities and transport—much of the text up to this point—to a manipulation of them through stress and strain. Semiconductors can be strained through a variety of techniques, with strained growth leading to a strained layer, and pattern definition leading to local strained region, being the most common. Strain changes bandstructures and interface bandedge energies, distorts and warps bands, removes degeneracies, affects scattering and thus changes a variety of properties. Following a continuum description of stress-strain relationships, effects of stress—biaxial, hydrostatic and uniaxial—are analyzed for bandstructure and transport in electron bands, light-hole bands, heavy-hole bands and split-off bands in group IV and group III-V semiconductors. Transport effects can be particularly strong in quantum-confined conditions, where changes in density of states can be significant, along with other bandstructure and scattering changes.