SOFA (Simulation Open Framework Architecture) is an open-source C++ library primarily targeted at interactive computational medical simulation. SOFA facilitates collaborations between specialists from various domains, by decomposing complex simulators into components designed independently and organized in a scenegraph data structure. Each component encapsulates one of the aspects of a simulation, such as the degrees of freedom, the forces and constraints, the differential equations, the main loop algorithms, the linear solvers, the collision detection al- Authors Suppressed Due to Excessive Length gorithms or the interaction devices. The simulated objects can be represented using several models, each of them optimized for a different task such as the computation of internal forces, collision detection, haptics or visual display. These models are synchronized during the simulation using a mapping mechanism. CPU and GPU implementations can be transparently combined to exploit the computational power of modern hardware architectures. Thanks to this flexible yet efficient architecture, SOFA can be used as a test-bed to compare models and algorithms, or as a basis for the development of complex, high-performance simulators.

To control morphogenesis, molecular regulatory networks have to interfere with the mechanical properties of the individual cells of developing organs and tissues, but how this is achieved is not well known. We study this issue here in the shoot meristem of higher plants, a group of undifferentiated cells where complex changes in growth rates and directions lead to the continuous formation of new organs. Here, we show that the plant hormone auxin plays an important role in this process via a dual, local effect on the extracellular matrix, the cell wall, which determines cell shape. Our study reveals that auxin not only causes a limited reduction in wall stiffness but also directly interferes with wall anisotropy via the regulation of cortical microtubule dynamics. We further show that to induce growth isotropy and organ outgrowth, auxin somehow interferes with the cortical microtubule-ordering activity of a network of proteins, including AUXIN BINDING PROTEIN 1 and KATANIN 1. Numerical simulations further indicate that the induced isotropy is sufficient to amplify the effects of the relatively minor changes in wall stiffness to promote organogenesis and the establishment of new growth axes in a robust manner.

The link between genetic regulation and the definition of form and size during morphogenesis remains largely an open question in both plant and animal biology. This is partially due to the complexity of the process, involving extensive molecular networks, multiple feedbacks between different scales of organization and physical forces operating at multiple levels. Here we present a conceptual and modeling framework aimed at generating an integrated understanding of morphogenesis in plants. This framework is based on the biophysical properties of plant cells, which are under high internal turgor pressure, and are prevented from bursting because of the presence of a rigid cell wall. To control cell growth, the underlying molecular networks must interfere locally with the elastic and/or plastic extensibility of this cell wall. We present a model in the form of a three dimensional (3D) virtual tissue, where growth depends on the local modulation of wall mechanical properties and turgor pressure. The model shows how forces generated by turgor-pressure can act both cell autonomously and non-cell autonomously to drive growth in different directions. We use simulations to explore lateral organ formation at the shoot apical meristem. Although different scenarios lead to similar shape changes, they are not equivalent and lead to different, testable predictions regarding the mechanical and geometrical properties of the growing lateral organs. Using flower development as an example, we further show how a limited number of gene activities can explain the complex shape changes that accompany organ outgrowth.