Thomas C.T. Michaels - University of Oxford #
Nucleated polymerisation with association #
The formation of protein filaments is a phenomenon that underlies a
range of functional and pathological processes in nature, including the
generation of functional scaffolds but also the development of 
pathological aggregates in the context of Alzheimer's disease and 
related disorders.
Kinetic studies have proved to be a particularly powerful tool to 
elucidate the mechanisms and rates underlying this important biological 
selfassembly process. The master equation describing filamentous
growth
has been known since the pioneering work by Oosawa in the 1960 and
this framework and its extensions to secondary nucleation processes have
been shown to describe the kinetics of protein filament
 growth 
accurately
under a wide variety of different
 conditions and for very different
protein systems. The study of the equilibrium behaviour of such systems
has, however been complicated by the fact that the long time limit of
the kinetic equations typically does not describe thermodynamic 
equilibrium as the master equation does not satisfy detailed balance. We 
have
addressed this problem by combining nucleated polymerisation with living 
polymerisation to generate a master equation that
satisfies
 detailed
balance in the steady state. In our kinetic model for nucleated growth
filamentous structures can undergo association, in addition to 
elongation
and fragmentation or other secondary processes. Within our approach we
take into account all possible association and fragmentation processes 
between clusters of any size. We explore the physical features of the 
model
and give self-consistent analytical solutions to the growth kinetics and
length distribution and identify the key time scales that describe 
relaxation to equilibrium. We test the validity of our analytical 
results against
numerical solutions of the corresponding equations.
<br/><br/>
In collaboration with T.P.J. Knowles.