SCIENCE AT THE EDGE SEMINAR

                         Friday, February 2, 2001
            11:30am-12:30, Room 224 Physics-Astronomy Building
                         (Refreshments at 11:15am)


                      WALTER WHITELEY, YORK UNIVERSITY

                      Rigidity of Molecular Structures


Abstract:  For the last 150 years, people have struggled with variants
of a basic unsolved problem in geometry and combinatorics:  Which graphs 
of vertices and edges will form rigid frameworks in 3-space?

Over the last 150 years, geometers and engineers have developed a solid
understanding of the projective geometry and combinatorics of rigid
frameworks in the plane.  In the last thirty years, this unsolved
problem in 3-D has reappeared in many applications, most recently in the
flexibility and rigidity of molecules.  Some properties of a protein may
be predicted from the shape of the folded protein and the answers to
questions such as:
     Which sections of a protein are likely to be rigid? 
     and  How will the entire protein move?
Geometric issues in disease and treatment, such as protease inhibitors
and Mad Cow Disease highlight the critical role of shape and rigidity in
understanding and modifying protein function.  

A team at Michigan State University has developed the FIRST (Floppy
Inclusion and Rigid Substructure Topography) computer program to rapidly
predict rigidity and flexibility from a graph for the folded protein.  A
key step in verifying this algorithm corresponds to a conjecture of T-S
Tay and myself (1984) about a specialized class of frameworks.  We
present some history and background for the solved and unsolved problems
about frameworks in 3-space with simple illustrations (including
physical models).  We will then discuss the conjecture / desired
property for spatial frameworks which falls between a solved special
case and the unsolved general problem.  We indicate some recent results
for special cases of the conjecture.