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Geometric patterns link structure to function in leaves
The structure and delivery of nutrients is provided by the Vascular system in the leaf. With the use of fluorescent dye and time-lapse photography, details of nature’s mathematical formula for survival begin to emerge.
Mother Nature is tough to beat when it comes to optimizing form with function.
Marcelo Magnasco, a mathematical physicist at Rockefeller University in New York, says “When looking at the detail you can see beautiful arrangements of impinging angles where the big veins meet the little veins and how well they are arranged”.
Magnasco and his colleague, physicist Eleni Katifori, analyzes the architecture of leaves by finding geometric patterns that link biological structure to function with support from the National Science Foundation (NSF).
They studied a specific vascular pattern of loops within loops found in many leaves down to the microscopic level. It is a pattern that can neutralize the effect of a wound to a leaf, such as a hole in its main vein. Nutrients bypass the hole leaving the leaf completely intact.
Something that looks pretty is pretty for good reason. It has a well defined and elegant function. We scan the leaves at extremely high resolution and reconstruct every single little piece of vein, according to the reseearchers.
Magnasco and Katifori digitally dissect the patterns, level by level. “It was very hard to find a unique way of enumerating how they are ordered. Our idea was to start at the very bottom, counting all of the individual little loops,” recalls Magnasco.
“This research is a unique interdisciplinary partnership in which physics is used to address biological problems. We believe the mathematical and physical sciences will play a huge role in biomedical research in this century,” says Krastan Blagoev, director for the Physics of Living Systems program in NSF’s Mathematical and Physical Sciences Directorate, which funded the research.
Magnasco says this research is a starting point for us to understand other systems that branch and rejoin. This includes everything from river systems to neural networks and even malignant tumors. When a tumor becomes malignant it vascularizes, so this is extremely important for understanding how these things work.
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