Group IV heteroadamantanes: synthesis of Si6Sn4 and site-selective derivatization of Si6Ge4.

The mixed heteroadamantanes Si6Ge4 and Si6Sn4 are readily accessible from Me2ECl2/Si2Cl6/cat. Cl- (4 × EMe2, 2 × SiCl2, 4 × Si-SiCl3 vertices; E = Ge, Sn). Different from Si6Ge4, two skeletal isomers are formed in the case of Si6Sn4. Site-selective SiCl3-methylation of Si6Ge4 was achieved, leaving the SiCl2 groups untouched.

Dope it with germanium: selective access to functionalized Si5Ge heterocycles.

The Cl- diadduct [nBu4N]2[A·2Cl] of the mixed cyclohexatetrelane (SiCl2)5(GeMe2), A, is accessible from Me2GeCl2, 6 eq. Si2Cl6, and 2 eq. [nBu4N]Cl in one step (96%). Free, tenfold functionalized A can be released from the primary product by decomplexation with AlCl3 (78%). Insight into the assembly mechanism of [nBu4N]2[A·2Cl] and the reactivity of A is provided.

Mixed-Substituted Single-Source Precursors for Si1-xGex Thin Film Deposition.

A series of new mixed-substituted heteronuclear precursors with preformed Si-Ge bonds has been synthesized via a two-step synthesis protocol. The molecular sources combine convenient handling with sufficient thermal lability to provide access to group IV alloys with low carbon content. Differences in the molecule-material conversion by chemical vapor deposition (CVD) techniques are described and traced back to the molecular design. This study illustrates the possibility of tailoring the physical and chemical properties of single-source precursors for their application in the CVD of Si1-xGex coatings. Moreover, partial crystallization of the Si1-xGex has been achieved by Ga metal-supported CVD growth, which demonstrated the potential of the presented precursor class for the synthesis of crystalline group IV alloys.

Subvalent mixed SixGey oligomers: (Cl3Si)4Ge and Cl2(Me2EtN)SiGe(SiCl3)2.

(Cl3Si)4Ge (1; 91%) is accessible from GeCl4, the Si2Cl6/[nBu4N]Cl silylation system, and excess SiCl4. A key intermediate step involves Cl- sequestration with AlCl3 in the course of the reaction between the first-formed germanide [(Cl3Si)3Ge]- and SiCl4. The related adduct Cl2(Me2EtN)SiGe(SiCl3)2 (2; quantitative conversion) was prepared either by amine-induced cleavage of 1 or by a bottom-up synthesis starting from GeCl4 and Si2Cl6.

Optimizing micropattern geometries for cell shape and migration with genetic algorithms.

Adhesive micropatterns have become a standard tool to control cell shape and function in cell culture. However, the variety of possible patterns is infinitely large and experiments often restrict themselves to established designs. Here we suggest a systematic method to establish novel micropatterns for desired functions using genetic algorithms. The evolutionary fitness of a certain pattern is computed using a cellular Potts model that describes cell behavior on micropattern. We first predict optimal patterns for a desired cell shape. We then optimize ratchet geometries to bias cell migration in a certain direction and find that asymmetric triangles are superior over the symmetric ones often used in experiments. Finally we design geometries which reverse the migration direction of cells when cell density increases due to cell division.

Dynamics of Cell Ensembles on Adhesive Micropatterns: Bridging the Gap between Single Cell Spreading and Collective Cell Migration.

The collective dynamics of multicellular systems arise from the interplay of a few fundamental elements: growth, division and apoptosis of single cells; their mechanical and adhesive interactions with neighboring cells and the extracellular matrix; and the tendency of polarized cells to move. Micropatterned substrates are increasingly used to dissect the relative roles of these fundamental processes and to control the resulting dynamics. Here we show that a unifying computational framework based on the cellular Potts model can describe the experimentally observed cell dynamics over all relevant length scales. For single cells, the model correctly predicts the statistical distribution of the orientation of the cell division axis as well as the final organisation of the two daughters on a large range of micropatterns, including those situations in which a stable configuration is not achieved and rotation ensues. Large ensembles migrating in heterogeneous environments form non-adhesive regions of inward-curved arcs like in epithelial bridge formation. Collective migration leads to swirl formation with variations in cell area as observed experimentally. In each case, we also use our model to predict cell dynamics on patterns that have not been studied before.

Modeling cell shape and dynamics on micropatterns.

Adhesive micropatterns have become a standard tool to study cells under defined conditions. Applications range from controlling the differentiation and fate of single cells to guiding the collective migration of cell sheets. In long-term experiments, single cell normalization is challenged by cell division. For all of these setups, mathematical models predicting cell shape and dynamics can guide pattern design. Here we review recent advances in predicting and explaining cell shape, traction forces and dynamics on micropatterns. Starting with contour models as the simplest approach to explain concave cell shapes, we move on to network and continuum descriptions as examples for static models. To describe dynamic processes, cellular Potts, vertex and phase field models can be used. Different types of model are appropriate to address different biological questions and together, they provide a versatile tool box to predict cell behavior on micropatterns.

Dynamics of cell shape and forces on micropatterned substrates predicted by a cellular Potts model.

Micropatterned substrates are often used to standardize cell experiments and to quantitatively study the relation between cell shape and function. Moreover, they are increasingly used in combination with traction force microscopy on soft elastic substrates. To predict the dynamics and steady states of cell shape and forces without any a priori knowledge of how the cell will spread on a given micropattern, here we extend earlier formulations of the two-dimensional cellular Potts model. The third dimension is treated as an area reservoir for spreading. To account for local contour reinforcement by peripheral bundles, we augment the cellular Potts model by elements of the tension-elasticity model. We first parameterize our model and show that it accounts for momentum conservation. We then demonstrate that it is in good agreement with experimental data for shape, spreading dynamics, and traction force patterns of cells on micropatterned substrates. We finally predict shapes and forces for micropatterns that have not yet been experimentally studied.

Stochastic dynamics of small ensembles of non-processive molecular motors: the parallel cluster model.

Non-processive molecular motors have to work together in ensembles in order to generate appreciable levels of force or movement. In skeletal muscle, for example, hundreds of myosin II molecules cooperate in thick filaments. In non-muscle cells, by contrast, small groups with few tens of non-muscle myosin II motors contribute to essential cellular processes such as transport, shape changes, or mechanosensing. Here we introduce a detailed and analytically tractable model for this important situation. Using a three-state crossbridge model for the myosin II motor cycle and exploiting the assumptions of fast power stroke kinetics and equal load sharing between motors in equivalent states, we reduce the stochastic reaction network to a one-step master equation for the binding and unbinding dynamics (parallel cluster model) and derive the rules for ensemble movement. We find that for constant external load, ensemble dynamics is strongly shaped by the catch bond character of myosin II, which leads to an increase of the fraction of bound motors under load and thus to firm attachment even for small ensembles. This adaptation to load results in a concave force-velocity relation described by a Hill relation. For external load provided by a linear spring, myosin II ensembles dynamically adjust themselves towards an isometric state with constant average position and load. The dynamics of the ensembles is now determined mainly by the distribution of motors over the different kinds of bound states. For increasing stiffness of the external spring, there is a sharp transition beyond which myosin II can no longer perform the power stroke. Slow unbinding from the pre-power-stroke state protects the ensembles against detachment.