Very, very excited about our new interdisciplinary graduate training program at SU: , with co-PIs @LovelessRadio , @ZhenMa2046, @Castaneda_lab , and Teng Zhang. Folks can apply this winter for grad fellowships starting next year!.

We also plan to apply these methods to physical systems, either by fabricating computer-designed materials or by finding local design rules that can drive a system to an optimal configuration through physical learning. 12/.

One could use these techniques to design other features on the critical manifold. It also provides a framework for thinking about the critical manifold as a statistical ensemble to search for common features and order parameters of critical states. 11/.

We then compare these optimal networks with unoptimized configurations taken from random samples of the critical manifold. 10/

We find configurations with ideal structures, such as minimal fluctuations in edge lengths or tensions; or with enhanced elastic responses, by maximizing either the bulk or shear modulus at the critical point. 9/

Because we have an analytic parameterization for the critical manifold, we can straightforwardly use gradient descent methods to numerically find critical configurations that optimize any objective function. 8/.

We show that there is a particular quantity, which we call the geometric stress, that acts as natural degrees of freedom to parameterize a smooth manifold of states at the critical point for central-force networks. 7/

The geometric rigidity transition coincides with the appearance of a state of self-stress, which is a set of internal stresses that leave the system in equilibrium. But these critical configurations are very rare, so how do we find them? 6/

Previous work from our group ( has described this transition, but left open the question: what is the space of states at the geometric rigidity transition? How can we find configurations at the critical point that also have other desired properties? 5/.

Unlike the jamming transition in granular systems, which happens when there are enough contacts to constrain all infinitesimal motions of a system, this geometric rigidity transition occurs in underconstrained systems due to nonlinear effects at fixed network connectivity. 4/.

Confluent tissues and biopolymer networks such as collagen can change their stiffness by orders of magnitude with small changes to their structure. These systems tune internal parameters to cross this transition to fulfill specific functions 3/

Biological materials exhibit an incredible ability to adapt their mechanical properties by being poised at a geometric rigidity transition. We developed a framework for designing materials at this critical point that have other desired properties. 2/

Excited to highlight a new preprint spearheaded by grad student Tyler Hain @t_hainous, in collaboration with @csantangelo314, "Optimizing properties on the critical rigidity manifold of underconstrained central force networks" 1/.

Really looking forward to this Symposium!.

Our work confirms that slow tissue movements can generate forces that are significant enough to deform an organ, as the timescale of tissue relaxation is large. This suggests dynamical forces may be playing a role in many other developmental processes, too. We should look!.13/n.

In addition to altering lumen shape changes, are dynamical forces sufficient to change individual cell shapes to drive KV remodeling involved in LR patterning?. Yes, notochord ablation reduces the AP distribution as compared to controls. The 3D vertex model predicts this. 12/n

These shape changes are generic – they can also be seen in a simpler hydrodynamic model of a membrane surrounded by a highly viscous medium, also with anterior pushing forces and posterior pulling forces. 11/n

The experiments match the simulation predictions! In notochord ablation experiments, the lumen elongates along the anterior-posterior axis (RgAP/RgLRincreases), while posterior cells ablations extend the lumen along the left-right axis (RgAP/RgLR decreases). 10/n

We quantify KV shape by the ratio of the radius of gyration of the lumen along the AP and LR directions (RgAP/RgLR). In simulations, we mimic notochord (posterior cell) ablations by removing the pushing (pulling) forces, and find that the organ changes it shape significantly. 9/n.

In simulations, we identify a set of model parameters (star in phase diagram) that generate the lumen shape seen in control experiments, where KV is pushed from the anterior by the notochord (orange cells) and pulled by posterior cells (purple cells). 8/n