The
vascular system of a leaf provides its structure and delivers its
nutrients. When you light up that vascular structure with some
fluorescent dye and view it using time-lapse photography, details begin
to emerge that reveal nature’s mathematical formula for survival.

When it comes to optimizing form with function, it’s tough to beat Mother Nature.

“If
you begin looking at them in any degree of detail, you will see all of
those beautiful arrangements of impinging angles and where the big veins
meet the little veins and how well they are arranged,” says Marcelo
Magnasco, a mathematical physicist at Rockefeller University in New
York.

With
support from the National Science Foundation (NSF), Magnasco and his
colleague, physicist Eleni Katifori, analyze the architecture of leaves
by finding geometric patterns that link biological structure to
function.

They
study a specific vascular pattern of loops within loops that is found
in many leaves going down to the microscopic level. It’s a pattern that
can neutralize the effect of a wound to the leaf, such as a hole in its
main vein. Nutrients bypass the hole and the leaf remains completely
intact.

“Something
that looks pretty looks pretty for a really good reason. It has a well
defined and elegant function. We can scan the leaves at extremely high
resolution and reconstruct every single little piece of vein, who talks
to who, who is connected to who and so forth,” explains Magnasco.

Magnasco
and Katifori digitally dissect the patterns, level by level. “It was
very hard to get to a unique way of actually enumerating how they are
ordered. Then we hit on the idea that what we should do is 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, and it is our belief that the
mathematical and physical sciences will play a major 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 jumping off point for understanding other
systems that branch and rejoin, including everything from river systems
to neural networks and even malignant tumors. “When a tumor becomes
malignant it vascularizes, so understanding all of this is extremely
important for understanding how these things work,” says Magnasco.   
   

Source: National Science Foundation