Computational Physics Group

[edit] Some of the interesting goings-on in our group

1. How does a tissue grow?
2. Why don't cells just peel off?
3. How does a cell know which way is up... or front or back...?
4. Does squeezing a crystal make atoms "flow"?
5. Four derivatives?? Can I program that in my calculator?

[edit] How does a tissue grow?

The laws of Physics govern how mass is added or taken out, how momentum is gained or lost, and how energy increases or is dissipated. Growth and decay of biological tissue is, after all, just a rendering of these laws, made maddeningly complex by the many thousands of species involved, interacting by exchanging molecules, exerting forces on each other and trading energy. If we can, however, focus on the dominant processes involved, there is a story to tell...

Find out more from Harish Narayanan.

[edit] Why don't cells just peel off?

Try this experiment: Attach a piece of sticking tape to a flat surface, leaving enough to comfortably grip between your fingers. If you tug at the tape such that the portion stuck to the surface forms an angle of less than 90 degrees with the bit that ends in your fingers, it will peel right off. In the image above the short red streaks are focal adhesions, by which cells attach themselves to surfaces. The green filaments are actin fibers, by which the cell tugs on the focal adhesions in order to haul itself along the surface. Why, then, do the focal adhesions not peel off? Of course, they may be really sticky. Granted, maybe. But here's more: As the cell tugs on the focal adhesions with the actin fibers, the focal adhesions actually grow! Furthermore, the cell must pull on a focal adhesion for it to grow. Curioser and curioser... isn't it?

This mechanism is poorly understood except for the now self-evident fact that it must have something to do with the force that the actin fibers transmit to the focal adhesion. We are summoning up classical ideas of Thermodynamics and kinetics to understand this mystery. An understanding of this aspect of cell behavior has implications for cancer cell adherence to organs, and therefore to metastasis.

Joe Olberding works on this, along with a few other things.

[edit] How does a cell know which way is up... or front or back...?

Cells in in most solid tissues (muscles, tendons, skin) appear with a specific alignment. How does this develop? Now classical experiments show that when cells on a two-dimensional substrate are subject to stress, either by stretching the substrate if it is compliant, by subjecting them to a well-aligned flow, or by other means, they reorient and align themselves in preferred directions. The images above show that the initially random orientation of a group of human fibroblast cells changes to a pronounced alignment close to (but not exactly) the vertical when the substrate on which they rest is subjected to cyclic straining in the horizontal direction. What drives this orientation? Stress or strain, of course, but why? How fast does it happen? What are the underlying intracellular mechanisms that drive this process? These are questions that we seek to answer from the standpoint of Physics.

An understanding of these responses of cells to mechanical stimuli will have implications for mechanical inhibition of cancer cells and promotion of stem cell activity.

My co-workers on this problem are Simon Jungbauer and Ralf Kemkemer from Max Planck Institut fuer Metallforschung, Stuttgart.

[edit] Does squeezing a crystal make atoms "flow"?

Actually, yes. The image above from our work shows an interstitial defect in silicon. This is a so-called <1 1 0> interstitial, or the "dumbell" interstitial for obvious reasons. If the silicon crystal is subject to an external stress of a particular form and spatial distribution it becomes possible to modify the thermodynamics within the crystal so that the interstitial is forced to hop from one site to another in the crystal. Furthermore, the stress can make the defect hop faster or slower, responding like a marching troupe to a drummer. Why all of this should happen is due to a decidedly odd object called an activation volume tensor, which encodes a rigorous, mathematical description of how the defect distorts the crystal around itself. We have forged a combination of continuum elasticity, molecular and quantum mechanics, and kinetic Monte Carlo methods to tease out the great complexity of this dance.

Brian Puchala and Sungick Kim are the students working on this problem. Before them, Lori Bassman, Hashem Mourad and Mathieu Bouville worked on various aspects of it. This work has been supported by the National Science Foundation via grants numbered CMS0075989 and CMS0331016.

[edit] Four derivatives?? Can I program that in my calculator?

Nope. At least, not yet. The evolution of structure shown above is from a numerical solution of the Cahn-Hilliard Equation. It describes the evolution of binary solid or fluid mixtures, has been used in image processing, and even models planet formation. The difficulty is that such beauty does not come easy. The physics that one must model gives rise to 4 spatial derivatives in this time- and spatially-dependent partial differential (for purists, it is parabolic). Furthermore, it has nonlinearities and instabilities. We have been developing a class of numerical methods called Discontinuous Galerkin Finite Element Methods to treat these high-order spatial derivatives in a computationally-tractable manner. Problems with high-order spatial derivatives actually abound in Physics. We have previously developed these methods for strain gradient elasticity, damage, and now are working on strain gradient plasticity.

Jake Ostien currently works on Discontinuous Galerkin methods for strain gradient plasticity models. Before him, Luisa Molari developed these methods for strain gradient elasticity.