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.

2. Microtubule biology

Microtubule networks underlie the external plasma membrane and extend through the cy- tomatrix in nearly all eucaryotic cells. They are particularly prolific in neurons, where they play an important role with the aid of MAPs in the formation and function of both axonal and den- dritic projections Burgoyne, 1991; Alberts et al., 1994. The individual microtubules are assembled from smaller proteins tubulin dimers. Network structures are molded by the assembly process and also by a microtubule organizing center MTOC, influences exerted by bound MAPS, and environmental regulators. The assembly pro- cedure is unique: microtubules can grow by adding new tubulin dimers to a particular end and shrink by reversing this process. The assembly process thus gives microtubules an orientation within the cell. Whether assembly or disassembly occurs depends on the dimer con- formational state, classified as straight or curved. The straight state promotes assembly; the curved state promotes disassembly. The growth end of an assembling microtubule comprises a region of straight dimers called the lateral cap Fig. 1. Over time the lateral cap can decrease in size through conversion of older straight dimers to curved form by hydrolysis. If the entire cap is converted to curved dimers the microtubule will begin to disassemble, eventually disappearing altogether unless the cap can re-form. Re-forming the lateral cap on a disassembling microtubule called res- cue allows the structure to return to the assembly mode. The dynamic instability phenomenon dis- cussed previously follows from the interplay of cap disappearance and rescue. In the cell the MTOC adds an additional level of organization to dynamic instability by anchoring the non- growth end of the microtubules and thereby ori- enting the growth of the microtubule population as a whole. MAP interactions mold the popula- tion into different configurations by stabilizing individual microtubules and by subserving a vari- ety of other organizational roles. The growth dynamics described above provide four points of regulation. The first is the number of dimers that are converted from straight to curved in the lateral cap. This regulates the assem- bly characteristics of the individual microtubules. Second is the number of free dimers that can be incorporated into microtubules. Regulation of the binding efficiency of structure stabilizing MAPs is the third. The characteristics of the MAPs them- selves afford the fourth point of regulation. MAPs constitute a large family of proteins. Alterations in the MAP population can thus influence net- work organization and functionality. These possi- bilities for regulation suggest that microtubule networks are moldable systems that can develop into a variety of configurations capable of per- forming different tasks.

3. Model specification