Ciliary beating patterns map onto a low-dimensional behavioural space

Biological systems are robust to perturbations at both the genetic and environmental levels, although these same perturbations can elicit variation in behaviour. The interplay between functional robustness and behavioural variability is exemplified at the organellar level by the beating of cilia and flagella. Cilia are motile despite wide genetic diversity between and within species, differences in intracellular concentrations of ATP and calcium, and considerable environment fluctuations in temperature and viscosity. At the same time, these perturbations result in a variety of spatio-temporal patterns that span a rich behavioural space. To investigate this behavioural space we analysed the dynamics of isolated cilia from the unicellular algae Chlamydomonas reinhardtii under many different environmental and genetic conditions. We found that, despite large changes in beat frequency and amplitude, the space of waveform shapes is low-dimensional in the sense that two features account for 80% of the observed variation. The geometry of this behavioural space accords with the predictions of a simple mechanochemical model in the low-viscosity regime. This allowed us to associate waveform shape variability with changes in only the curvature response coefficients of the dynein motors.

A mechanochemical model recapitulates distinct vertebrate gastrulation modes

Gastrulation is a critical event in vertebrate morphogenesis driven by cellular processes, and characterized by coordinated multi-cellular movements that form the robust morphological structures. How these structures emerge in a developing organism and vary across vertebrates remains unclear. Inspired by experiments on the chick, we derive a theoretical framework that couples actomyosin activity to tissue flow, and provides a basis for the dynamics of gastrulation morphologies. Our model predicts the onset and development of observed experimental patterns of wild-type and perturbations of chick gastrulation as a spontaneous instability of a uniform state. Varying the initial conditions and a parameter in our model, allows us to recapitulate the phase space of gastrulation morphologies seen across vertebrates, consistent with experimental observations in the accompanying paper. All together, this suggests that early embryonic self-organization follows from a minimal predictive theory of active mechano-sensitive flows.

A Mechanochemical Model for the Simulation of Molecules and Molecular Crystals Under Hydrostatic Pressure

<div> <div> <div> <p>A novel mechanochemical method for the simulation of molecules and molecular crystals under hydrostatic pressure, the eXtended Hydrostatic Compression Force Field (X-HCFF) approach, is introduced. In contrast to comparable methods, the desired pressure can be adjusted non-iteratively and molecules of general shape retain chemically reasonable geometries even at high pressures. The implementation of the X-HCFF approach is straightforward and the computational cost is practically the same as for a regular geometry optimization. Pressure can be applied by using any desired electronic structure method for which a nuclear gradient is available. The results of X-HCFF for pressure-dependent intramolecular structural changes in the investigated molecules and molecular crystals as well as a simple pressure-induced dimerization reaction are chemically intuitive and fall within the range of other established computational methods. Experimental spectroscopic data of a molecular crystal under pressure are reproduced accurately. </p> </div> </div> </div>

A Mechanochemical Model for the Simulation of Molecules and Molecular Crystals Under Hydrostatic Pressure

<div> <div> <div> <p>A novel mechanochemical method for the simulation of molecules and molecular crystals under hydrostatic pressure, the eXtended Hydrostatic Compression Force Field (X-HCFF) approach, is introduced. In contrast to comparable methods, the desired pressure can be adjusted non-iteratively and molecules of general shape retain chemically reasonable geometries even at high pressures. The implementation of the X-HCFF approach is straightforward and the computational cost is practically the same as for a regular geometry optimization. Pressure can be applied by using any desired electronic structure method for which a nuclear gradient is available. The results of X-HCFF for pressure-dependent intramolecular structural changes in the investigated molecules and molecular crystals as well as a simple pressure-induced dimerization reaction are chemically intuitive and fall within the range of other established computational methods. Experimental spectroscopic data of a molecular crystal under pressure are reproduced accurately. </p> </div> </div> </div>

A hybrid stochastic–deterministic mechanochemical model of cell polarization

At the onset of cell locomotion, cells break symmetry to form well-defined cell fronts and rears through the process of cellular polarization. Using an in silico approach, we have identified one of the simplest quantitative frameworks as a possible mechanochemical mechanism for spontaneous cell polarization.