On the surface, biology and geometry are seemingly unrelated topics. The precise, highly-regulated study of lines, angles, and symmetry seems far removed from the study of moving, irregularly-shaped organisms. It can be difficult to imagine whether or not the two share any common ground.
If you look beneath the surface, you'll see that the two are actually quite intertwined with each other. A vast number of shapes and patterns make up the very fabric of life. From the fractal geometry of cancer cells and the intricate repeated patterns of the DNA helix to the newly discovered scutoid solids associated with organ formation and cell theory, the fascinating relationship between geometry and biology is woven into all of the details of life as we know it.
Many biological interactions - including protein binding, protein folding, and the like - are viewed as chemical bonding interactions. However, geometry drives much of these interactions, making research about protein binding and folding an exciting new step in the process of defining and replicating microscopic geometrical structures. As research continues, identifying new polymer structures and testing them under different chemical conditions and geometric shapes can hopefully provide ways to solve some of biology's more complex mysteries.
Geometry in the Lab
One of the many geometric shapes commonly found in biology is the sphere. In fact, spheres - in addition to rods and spirals - are one of the three ways scientists describe bacterial cell symmetry. Polymers are one of the many biological substances that exist in spherical shapes.
Under normal conditions, biological polymers such as carbohydrates, lipids, and proteins, are found in spherical shapes. When these polymers are exposed to certain laboratory conditions, they can denature - or, change shape or function. Most often, denaturation is caused by exposure to extreme heat or other stresses, such as exposure to chemical solutions or radiation.
Scientists at the University of Pennsylvania, in collaboration with the École Supérieure de Physique et de Chimie Industrielles de la Ville de Paris (ESPCI), recently conducted studies on the way that certain polymers change from spherical shapes to spirals when mixed with liquid crystals and exposed to another solvent. These changes, unlike some other biological geometric changes, occurred with no external energy applied to the solution. Moreover, they were reversible and reproducible and have provided data about what can be possible within a laboratory setting.
Protein Folding and Beyond
To identify how spheres were able to morph into spiral-shaped spindles, researchers developed mathematical models that isolated the way known geometrical shapes change. During this research, it became evident that the pattern was a loxodrome - an arc that follows a consistent angle as it travels across a sphere. Sailors from the 16th century used loxodromes to navigate ships across lines of latitude, allowing their compasses - and ships - to maintain a consistent bearing. Research has uncovered that biological structures also use loxodromes to change and revert shape.
During these studies, polymers responded to the introduction of a solvent by shrinking. In turn, the entire shape of the polymer shifted and twisted as each polymer chain along the original sphere's lines of latitude shortened. Spirals one micron wide - a hundred times narrower than a human hair - formed at the top of each spindle.
Uncovering how geometric patterns exist within proteins and can be manipulated provides huge opportunities to better understand how these proteins can function within our bodies.
Sources:
https://medium.com/show-some-stempathy/redefining-geometry-in-biology-a6e6c0bd2abf
