Date：3rd April(Mon)14:00-16:00
Venue：IIS,Dw-601
Invited Speaker： Prof. Alexander S. Mikhailov
(Department of Physical Chemistry,
Fritz Haber Institute of the Max  Planck Society, Berlin, Germany)

Title：

Slow ordered relaxation in random and designed elastic networks,  
single-molecule oscillators and prototypes of protein machines

ABSTRACT：

A molecular machine must perform well-defined internal motions,  
repeating them in a precise way each next operation cycle despite  
thermal noise and external perturbations. A macroscopic dynamical  
system with such properties would have a strong attractor  
representing a limit cycle. But continuous supply of energy, needed  
for limit-cycle oscillations, is not possible at the microscopic  
level. A molecular machine can receive chemical energy only in  
discrete portions, by binding some ligand particles. Therefore,  
ordered motions of such a machine must represent processes of  
relaxation after a sudden excitation. Generally, relaxation in a  
macromolecule with a large number of degrees of freedom is complex  
and highly sensitive to noise and perturbations. We show, however,  
that there is a special class of dynamical systems which is  
characterized by slow ordered relaxation. Starting from different  
initial conditions, their trajectories rapidly converge to a well- 
defined path leading to the equilibrium state. Thus, their relaxation  
resembles the dynamics of dynamical systems with limit-cycle  
attractors. Along the attractive relaxation path, a single effective  
"mechanical" coordinate, or a phase variable, can be introduced. Such  
special systems can be designed by running an artificial evolution  
process, as we demonstrate using the example of nonlinear elastic  
networks, representing an approximation for protein molecules. An  
elastic network model of a machine, whose cycles are operated by  
binding and detachment of a ligand, is constructed and discussed.  
These results are obtained together with Dr. Yuichi Togashi, a JSPS  
fellow in my group.