Mathematical Impressions: Symmetric Structures
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- เผยแพร่เมื่อ 18 ต.ค. 2024
- It is an unexplained fact that objects with icosahedral symmetry occur in nature only at microscopic scales. Examples include quasicrystals, many viruses, the carbon-60 molecule, and some beautiful protozoa in the radiolarian family.
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Mike
He also liked to spice things up, he made the pictures prettier and more complex than they actually were in real life.
The reason why icosahedral symmetry doesn't exist in the human scale has a few reasons according to my own understanding of materials science. My education background is chemistry, but my research area is surface chemistry. Therefore, I believe I am sufficiently qualified to offer some ideas to the question "why".
1) Surface area. This is a simple and obvious one for people in the biological sciences. You can calculate the surface area-to-volume ratio of large as compared to smaller spheres to easily tell that smaller objects have surprisingly larger surface areas. This not only underlies some of the basic principles of molecular recognition (e.g. ability to stick and fit surface receptors to illicit some kind of biological response), but also evolutionary advantages in how life interacts with each other on Earth (e.g. pollen from flowers). Your immune system has been shown to develop from a young age through this process as well by interacting with the invasion of foreign particles, viruses, bacteria...etc..
2) Transition from Statistical Thermodynamics to Quantum Mechanics. Almost all natural systems (with the exception of looking down to the nanoscale structures of < 5 nm) are dominated by thermodynamic forces (where the laws of thermodynamics apply) in what we chemists call the macroscale. However, if you investigate nanostructures in a carefully controlled (isolated) system, quantum effects tend to dominate (e.g. quantum confinement in nanoparticles). When scientists start to characterize individual particles (even molecules), you can say that they are in the microscale. What's so special about quantum mechanics? Well...in nanoparticles as an example, research has shown that you can manipulate the emission of light (called fluorescence) simply by changing the size of the particle. However, it's not that simple because surface structures (e.g. sometimes defects) can modulate the optical behavior of emission as well. The microscopic structures are in microns, but there are also finer structures in the nanoscale. In physical sciences, we see light as an electromagnetic wave thus having an energy per photon capable of being quantified. This basically underlies the fundamentals of photonic materials research, where people investigate the basic principles of light-to-matter interactions.
+YoAddicts From a chemistry/biochemisty background, I can also add that any structure made by lifeforms is done in an iterative manner. An intriguing theory on morphogenesis is the Turing model. Basically it states that morphogenesis occurs via a reaction-diffusion process (simply put, off signals and on signals compete, but travel at different rates, which causes a wave-like interference pattern where some signals are on and some signals are off). As an organism or structure grows, it either gets bigger or changes shape - both can affect the wave-like pattern of "on" and "off." This theory has been used to explain and model how some animals can have spots and stripes when juvenile, but be "plain" when adult. It has also been used to model how hands are formed from a uniform matrix of (mesenchymal) cells. However, an interesting observation (not proven) is that the larger something becomes, the simpler it becomes because the areas/volumes that are "on" or "off" become insignificant in comparison to the area/volume of the organism, or because the interference becomes destructive everywhere and thus terminates morphogenesis.
It is also easier to produce something spherical than to produce an icosahedon when talking about a few billion cells...
+Larzsolice Note, my description of Turing morphogenesis is horrible - it is not as simple as that but I used an oversimplification to make it more accessible to the casual reader.
Larzsolice Thank you for the thought provoking comment. I have never heard of the Turing model before, but now I am interested in reading about it in my spare time. The fact that ideas can be exchanged across disciplines is exactly why I'm into interdisciplinary research. Don't worry about oversimplification as it is a common occurrence in social media. I think many explanations in science are just too complex to only communicate in the verbal form. That's part of the reason why we have to write a thesis to document down the thought process. I consider social media writing close to the verbal form.
I would like to add that what I typed above isn't perfect either. Thermodynamic effects still exist in the nanoscale scale if nanoparticles are dispensed in a liquid medium. One of the ways to tell is just change the temperature of the medium and record the full width half maximal (fwhm) of absorption, excitation and fluorescence spectra. Of course, it is more complicated than that because of colloidal effects (e.g. DLVO theory). Furthermore, characterization of the optical effects may be possible using the Boltzmann distribution, which they may also be derived by the Einstein coefficients & the radiation density by Planck's black body radiation law. In research, many ideas are possible theoretically but not experimentally. However, some of the concepts from physics used in chemistry are sometimes quite useful in understanding chemical systems. For example, to exclude thermodynamic effects, physicists would use a vacuum and control their experiments at low temperatures to study quantum effects. I am not going into this as I am slowly moving into the realm of quantum biology. I am not a physicist. Does quantum mechanics exist in biological systems? To my knowledge, this is the big question in this new area of research which there are likely more questions than answers at the moment.
YoAddicts
While it is difficult to pin down quantum effects in biology, there is one exceptional case: chlorophyll. It captures light and transduces the energy in such an unimaginably efficient manner, that the only way to describe it is one quantum at a time. Unfortunately this is difficult to prove or model. That leads to the possibility of other quantum effects in electron transfer chains, but they tend to be multi-component systems so you can't isolate them and feed in one electron at a time. However, many enzymes that have metal centres in their active sites work through orbital overlap, which is a quantum process. While the field of bioinorganic chemistry does not deal explicitly with quantum mechanics, most of the phenomena rely on solutions to the Schrodinger equation for the metal involved and the molecular orbitals of the ligands and the substrates.
I believe that the reason why there arnt any human sized natural icosahedra, is the same reason why its only on the molecular level, because its part of the 5 Platonic solids and they are the starter shapes, it would make sense that if we were created by small particles , because those particle are the starter object it would make sense that they would be shaped like one of the starter shapes. Maybe the coral we see today did start as one of the Platonic solids and then when it grew it changed its shape to the ones we see today