Microtubule biology Directory UMM :Data Elmu:jurnal:B:Biosystems:Vol55.Issue1-3.2000:
selection acting on MAPs. The question addressed here is whether learning can occur on an individ-
ual cell level within a single life cycle. The model to be presented combines an empiri-
cally motivated growth mechanism with a general but abstract representation of signal processing.
The growth mechanism implements the low level dynamics of microtubule assembly to simulate
what is sometimes referred to as dynamic instabil- ity Wordeman and Mitchison, 1994. This term
refers to the fact that the net mass of the micro- tubule population can be relatively constant de-
spite continual assembly and disassembly of individual microtubules. Here we view dynamic
instability as a stochastic search mechanism that modifies the signal processing. The search can
continue, in a more fine tuned fashion, even if microtubule assembly and disassembly is frozen,
since MAP bindings can still change. Representa- tion of signal processing is more problematic.
Many modes are possible, and could even co-ex- ist; but the experimental situation is unclear.
Our choice is to treat the microtubules as strings of coupled oscillators on a discrete time
scale and to allow MAPs to link the oscillations in neighboring microtubules. The vibratory or
wave dynamics serves to combine input signals in space and time. Input signals are introduced by
readin MAPS, combined in space and time by the vibratory dynamics of the microtubules, and ex-
tracted by readout MAPs. Linker and modulating MAPs serve to tune the vibratory dynamics. The
coupled oscillator representation can be thought of as a highly simplified field model that could be
particularized to a wide variety of specific mecha- nisms. For the present purposes the important
point is that the microtubule network serves as a medium of signal integration.
The growth dynamics and signal processing are coupled by a learning mechanism to be referred to
as adaptive self-stabilization. The term is intended to suggest negative feedback acting on structure
and through this on the signal processing perfor- mance. A microtubule network is first generated
by the growth dynamics. The information pro- cessing capabilities of the network are then evalu-
ated relative to a training set of patterns. The growth parameters are changed in a manner that
depends on performance. If the network performs well only a small amount of microtubule growth
or variation in MAP distribution is allowed. If it performs poorly then the structure is allowed to
be more dynamic, commensurate with the fact that the error signal should be greater. The MAP
binding affinity in a sense plays the role of tem- perature in simulated annealing; increase and de-
crease in binding affinity corresponds to increase and decrease in temperature. When the system
reaches an adequate level of learning the micro- tubule structure is frozen. Further learning relies
on variations in MAP distribution that would in principle occur through diffusional search.