Modulation theory for pattern forming systems with a spatial 1:2-resonance.

It is the purpose of this paper to justify the use of modulation equations for pattern forming systems in the case of multiple Turing instabilities with critical wave numbers having a ratio 1:2 by proving approximation results, presenting attractivity results, and discussing the existence of modulating fronts.

Expression of keratinocyte biomarkers is governed by environmental biomechanics.

In solid body tissues, environmental biomechanics is indispensable for tissue homeostasis. While characteristics of homeostasis include morphogenesis, proliferation and differentiation, the influences through biomechanics in corneal keratinocytes are poorly understood. Here we show for the first time that corneal keratinocytes, established in a defined biomechanical microenvironment of micropatterned soft pillars, exhibit favoritism of late and terminal differentiation at large pillar patterns of 11 μm with matched small 5 μm arrays.