BioSystems 55 2000 47 – 58
Adaptive information processing in microtubule networks
Jeffrey O. Pfaffmann, Michael Conrad
Department of Computer Science, Wayne State Uni6ersity, Detroit, MI
48202
, USA
Abstract
Microtubule networks provide a wide range of microskeletal and micromuscular functionalities. Evidence from a number of directions suggests that they can also serve as a medium for intracellular signaling processing. The model
presented here comprises an empirically motivated representation of microtubule growth dynamics, an abstract representation of signal processing, and a feedback learning mechanism that we refer to as adaptive self-stabilization.
The growth model mimics the dynamic instability picture of microtubule formation and decomposition, but as modulated by the binding activity of microtubule associated proteins or MAPs. The signal processing submodel
treats each microtubule as a string of linked discrete oscillators capable of propagating signals that are introduced, manipulated, and extracted by bound MAP activity. Adaptive self-stabilization is essentially feedback acting on signal
processing capabilities via the growth dynamics. The network is presented with a training set of patterns. If the input – output behavior is satisfactory MAP binding affinity increases, thereby stabilizing the network structure;
otherwise the binding affinity decreases, allowing for more structural variation. The results obtained suggest that adaptive capabilities are practically inevitable in microtubule networks, a conclusion strengthened by the fact that the
signal processing and growth dynamics mechanisms available in nature are undoubtedly much richer than those represented in the model. © 2000 Elsevier Science Ireland Ltd. All rights reserved.
Keywords
:
Microtubule signal processing; Adaptive self-stabilization; Dynamic instability; Adaptive information processing www.elsevier.comlocatebiosystems
1. Introduction
Microtubules are polymacromolecular fibers that are instrumental in a wide variety of pro-
cesses in eucaryotic cells: mitosis, axonal trans- port, organelle organization and more generally
for structural integrity and dynamic form. The specific functions performed depend on auxiliary
proteins microtubule associated proteins, or MAPs for short that strongly influence the struc-
ture of the fibrous network and its interactions with membranes and other components of the
cytomatrix Matus, 1988. It is likely that micro- tubules also provide a medium for long range
intracellular signaling Kirkpatrick, 1979; Mat- sumoto and Sakai, 1979; Liberman et al., 1982,
1985; Hameroff and Watt, 1982; Hameroff, 1987; Conrad, 1991. Various adaptation mechanisms
have also been proposed Conrad et al., 1989; Conrad, 1990; Rasmussen et al., 1990; Chen and
Conrad, 1994; Ugur and Conrad, 1997. Adapta- tion on a phylogenetic time scale could easily
occur through population based variation and
Corresponding author. E-mail address
:
conradcs.wayne.edu M. Conrad 0303-264700 - see front matter © 2000 Elsevier Science Ireland Ltd. All rights reserved.
PII: S 0 3 0 3 - 2 6 4 7 9 9 0 0 0 8 2 - 9
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
