Models for molecular computation: conformational automata in the cytoskeleton

Models for Molecular Computation:

Conformational Automata in the Cytoskeleton

Stuart R. Hameroff, University of Arizona Judith E. Dayhoff, University of Maryland Rafael Lahoz-Beltra, Complutense University of Madrid Alexei V. Samsonovich, University of Arizona Steen Rasmussen, Los Alamos National Laboratory and the Santa Fe Institute

odern computing is evolving toward smaller structures, faster process- ing, and parallel and adaptive architectures. Computation with protein conformational changes can provide small structures (nanometers), (nanoseconds), sei€-assembly. phase transitions, and adaptive restruc-

turing. The disadvantages of protein-based computers include the difficulty of devising an interface. sensitive dependence on a “biological” environment, and susceptibility to degradation, senescence, and infection. Nevertheless, protein- based computing offers the best approach to human cognitive equivalence.

In this article. we describe the structure and conformational dynamic changes that occur in cytoskeletal proteins within living cells and evidence for their participation in computational processing. We discuss cellular automata (see the sidebar), in which lattice subunits with discrete states interact only with nearest neighbors. Simple rules governing subunit neighbor interactions can lead to complex behavior capable of computation. We show how cellular (molecular) automata may be implemented in the conformational relationships among neigh- boring protein subunits of cytoskeletal polymers including microtubules, and how microtubule conformational automata networks may signal, adapt, recognize, and subserve neural-level learning. Conformational automata in microtubules and cytoskeletal networks may be the computational medium within living cells.

This article proposes within

networks of filamentous polymers

in the cell cytoskeleton. Microtubules and the cytoskeleton

Information can be represented and

Interiors of living cells are structurally and dynamically organized by networks of interconnected protein polymers, as shown in Figure 1 .I Collectively termed the cytoskeleton because of their structural support, these networks also orchestrate and control dynamic cellular activities. The cytoskeleton consists of microtubules (MTs), actin microfilaments, intermediate filaments, and an organizing complex called the centrosome.? Parallel-arrayed MTs are interconnected by cross-bridging proteins (MT-associated proteins, or MAPs) to other MTs, organelles, filaments, and membranes to form dynamic networks. In addition to structural cross-linking MAPs, contractile or enzymatic MAPs may be attached to MTs at specific sites. These MAP-MT attachments may be irregular, but they often form periodic, superhelical patterns on MT surfaces (see Figure 1’ and Figures 2a through 2h3)).

transmitted via propagated

conformational changes of the

polymers’ subunits.

COMPUTER 30 0018-9162/9?/1100-0030$03.00 1992 IEEE

Cellular automata

Computation involves interactive signals or patterns in a lattice structure. Von Neumann described such sys- tems (which include computers as special cases) as cel- lular automata, which consist of a large number of identi- cal cells connected in a uniform pattern. The essential features of cellular automata (of which Conway’s Game of Life is one popular example) are the following:

(1) At a given time, each cell is in one of a number of finite states (usually two for simplicity).

(2) The cells are organized according to a fixed geom- etry.

(3) Each cell communicates only with other cells in its neighborhood; the size and shape of the neighborhood are the same for all cells.

(4) There is a universal clock. Each cell may change to a new state (or “generation”) at each tick of the clock, de- pending on its present state and the states of its neigh- bors.

The neighbor “transition” rules for changing states, though simple, can lead to complex, dynamic patterns manifesting chaos, fractal dimensions, partial differential equations, and computation. Patterns that move through the lattice unchanged are called gliders; von Neumann proved mathematically that gliders traveling through a sufficiently large cellular automaton can solve virtually any problem.

Figure 1. Electron micrograph of quick-frozen, deep- etched neuronal MTs polymerized with MAPS. Scale bar: 100 nm. (Reproduced with permission from Hirokawa.’)

Cellular automata are theoretically advantageous for molecular computing because the internal connections are intrinsic to.the material, external connections need only occur in one limited region, and computation can occur by local interactions with speed dependent on the clocking frequency. Conrad’ used the concept of “molecular” au- tomata within neurons as an information processing sys- tem subserving the brain’s synaptic connectionism. We have applied cellular (molecular) automata principles (us- ing Frohlich’s coherent 1 0-9- to 1 0-”-second excitations as a clocking frequency) to the dynamic conformational states of tubulin within cytoskeletal microtubules. We hope to understand and explain real-time control, self-or- ganization, communication, and computation in living cells, and to propose precursors to molecular computing paradigms.

Reference

1. M. Conrad, “Molecular Automata,” in Lecture Notes in Biomathe- matics, V014: Physics and Mathematics of the Nervous System, M. Conrad, W. Guttinger, and M. Dal Cin, eds., Springer-Verlag, Heidelberg, Germany, 1974, pp. 419-430.

Figure 2. Experimentally observed patterns of MAP at- tachment sites on MTs (a-h).3 Theoretically calculated patterns of MT phonon-mode maxima (i-t). Experimental patterns match the theoretically predicted patterns, either exactly or approximately.

November 1992 31

T 8 1 1

i m

U

Y t

Figure 3. MT structure from X-ray crystallography4 (a). Tubulin subunits are 8- nm dimers composed of a and p monomers. MT automata neighborhood (b): left, definition of neighborhood dimers; center, a and p monomers within each dimer; right, distances in nanometers and orientation among lattice neighbors.

Contractile MAPs such as dynein and kinesin participate in cell movement as well asintraneuronal (axoplasmic) trans- port. which moves material and plays a

major role in maintaining and regulat- ing synapses. MAPs that form structur- al bridges stabilize MTs and prevent their disassembly. and may be phospho-

rylated and impart energy into the cy- toskeleton. Thus, MAP-MT cytoskele- tal networks determine cell architec- ture and dynamic functions essential to the living state (mitosis, growth, differ- entiation, movement, synapse forma- tion and function, and so on).

Of the filamentous structures that make up the cytoskeleton, MTs are the best characterized. As Figure 3a shows, MTs are hollow cylinders 25 nanome- ters in diameter whose walls are 13 chains of subunit proteins known as t ~ b u l i n . ~ Each tubulin subunit is a polar, 8-nm dimer that consists of two slightly dif- ferent classes of 4-nm monomers (mo- lecular weight 55,000) known as a and p tubulin. Each dimer (as well as whole MTs) has dipoles with negative charges localized toward a m0nomers.j Dimers self-assemble into MTs in an entropy- driven process that can quickly change by MT disassembly and reassembly in another orientation (dynamic instabili- ty). The tubulin dimer subunits within MTs are arranged in a slightly twisted hexagonal lattice, resulting in differing

The cytoskeleton and information processing

The cytoskeleton provides structural support and trans- port. An additional role as the cell’s on-board computer is suggested by evidence that links the cytoskeleton with cognitive function.’ * For example, production of tubulin and MT activities correlate with peak learning, memory, and experience in baby chick brains. When baby rats first open their eyes, neurons in their visual cortex begin pro- ducing vast quantities of tubulin. Selective destruction of animal brain MTs by the drug colchicine causes defects in learning and memory that mimic the symptoms of Alzhei- mer’s disease (in which the neuronal cytoskeleton entan- gles).

comes from studies of long-term potentiation (LTP), a form of synaptic plasticity that serves as a model for learning and memory in mammalian hippocampal cortex. A dendrite-specific MAP called MAP2 cross-links MTs, is essential for LTP, and consumes a large proportion of brain biochemical energy (phosphorylation/dephosphory- lation). MAP2 and other cytoskeletal structures are linked to membrane receptors and their activities by “second messengers” including G proteins, cyclic AMP, calcium ions, and protein kinases. Activation of LTP postsynaptic receptors induces rapid dephosphorylation of dendritic MAP2. Excitatory neurotransmitters cause rearrangement of MAP connections on MTs. Lynch and Baudry3 found that LTP depends on rearrangement of the subsynaptic cytoskeleton, and implicated a calcium-activated proteo- lytic enzyme “calpain” in the initial step: cytoskeletal cleavage and digestion. Calpain degrades MAP2 as well

Other evidence for cytoskeletal involvement in cognition

as other cytoskeletal proteins, and calpain inhibitors block LTP. Friedrich4 formalized a model in which learning and memory are structurally represented in a more complex and interconnected subsynaptic cytoskeleton.

Cytoskeletal destruction from excessive calpain activity may be involved in irreversible neuronal injury from hy- poxia (lack of oxygen) mediated by excessive calcium in- flux. In animals exposed to brain hypoxia, the reduction in dendritic MAP2 correlates with the degree of cognitive damage, and calpain inhibitors may protect neurons from hypoxia.

Tubulin subunits in closely arrayed MTs have a density of about 1017 per cubic centimeter, close to the theoretical limit for charge separation. Thus, cytoskeletal polymers have maximal density for information representation by charge, and the capacity for dynamically coupling that in- formation to mechanical and chemical events via cooper- ative conformational states.

References

1. S. Rasmussen et al., “Computational Connectionism Within Neu- rons: A Model of Cytoskeletal Automata Subsetving Neural Net- works,’’ Pbysica D, Vol. 42, Nos. 1-3, June 1990, pp. 428-449.

2. S.R. Hameroff, Ulfimafe Computing: Biomolecular Consciousness and Nanotechnology, Elsevier-North Holland, Amsterdam, 1987.

3. G . Lynch and M. Baudry, “Brain Spectrin, Calpain, and Long- Term Changes in Synaptic Efficacy,” Brain Research Bull.. Vol. 18, No. 6, June 1987, pp. 809-815.

4. P. Friedrich, “Protein Structure: The Primary Substrate for Memo- ry,” Neuroscience, Vol. 35, No. 1, 1990, pp. 1-7.

neighbor relationships among each sub- unit and its six nearest neighbors.

Tubulin undergoes conformational changes induced by hydrolysis of bound high-energy phosphate molecules, con- formational changes of neighboring pro- teins, and other factors. Genes for ct and p tubulin are complex and give rise to varying tubulin primary structure (for example, at least 17 different p tubulins can exist in mammalian brain MTs). Tubulin in MTs can also be modified by binding various ligands and MAPs, or enzymatic addition or removal of ami- no acids (posttranslational modifica- tion), or conformational state changes. Consequently, the number of different possible tubulin state combinations (and thus information capacity) within MTs is enormous. (See the sidebar entitled “The cytoskeleton and information pro- cessing.”)

Molecular automata in microtubules

Single microtubule automata. Molec- ular automata require a lattice whose subunits can exist in two or more states at discrete time steps, and transition rules that determine those states among lattice neighbor subunits. Tubulin con- formations within MT lattices can pro- vide such states, and neighbor-tubulin interactions (represented by dipole cou- pling forces) may provide appropriate transition rules. A rough estimate for the time steps, assuming one coherent “sound” wave across the MT diameter (@ - 25 nm) and Vhound = lo3 meters per second, yields a clocking frequency of approximately 4 x 1O’O Hz, and a time step of 2.5 x lo-” second. Thus, Frohli- ch’s coherent excitations (see the side- bar entitled “Protein conformational dynamics”) can provide a “clocking fre- quency” for MT conformational autom- ata.

Conformation of individual tubulin subunits at any given time depends on “programming” factors including ini- tial conformational state; primary ge- netic structure; binding of water, ions, or MAPs; bridges to other MTs; post- translational modifications; phospho- rylation state; and mechanical and elec- trostatic dipole forces among neigh- boring subunits. We consider only elec- trostatic dipole forces among neighbor- ing tubulin subunits. Figure 3b shows a

Protein conformational dynamics

In their natural state, proteins are dynamic structures that undergo confor- mational motions over a wide range of time and energy scales. Conforma- tional changes related to protein function occur in the nanosecond sec- ond) to IO-picosecond (1 0-j’ second) time scale. Related to cooperative movements of protein subregions and charge redistributions, these changes are linked to protein function (signal transduction, ion channel opening, en- zyme action, and so on) and may be triggered by factors including phospho- rylation, adenosine or guanine triphosphate (ATP or GTP) hydrolysis, ion fluxes, electric fields, ligand binding, and neighboring protein conformational changes.

In the case of tubulin within MTs, we propose that such programmable and adaptable states can represent and propagate information. Vassilev, Kanazirska, and Tienl experimentally showed signaling in MT tubulin. Theo- retical approaches that can describe such propagation include elastic self- trapping modes such as solitons, coherent phonons, and polarization waves. Solitons are quantized packets of energy (and information) that travel with minimal dissipation in water (canal waves, ocean tidal waves), optical fibers (carrying information such as telephone data), and other media. Conforma- tional solitons have been predicted to occur in biological materials such as actin-myosin, DNA, and MTs. These theoretical cases predict that energy is supplied by dephosphorylation or hydrolysis of ATP or GTP, and that the en- ergyhformation packet is used in muscle contraction, DNA replication, and MT signaling and polymerization.

Frohlich2 proposed that protein conformational changes are coupled to charge redistributions such as dipole oscillations within specific hydrophobic protein regions. (Such protein hydrophobic regions are also where general anesthetic gas molecules are thought to act by preventing protein conforma- tional responsiveness.) Frohlich further proposed that a set of proteins con- nected in an electromagnetic field such as within a polarized membrane (or polar polymer like a microtubule) would be excited coherently if biochemical energy such as protein phosphorylation or ATP or GTP hydrolysis were sup- plied. Coherent excitation frequencies on the order of IO9 to 10” Hi! (the time domain for functional protein conformational changes, and in the micro- wave or gigahertz spectral region) were deduced by Frohlich, who termed them acousto-conformational transitions, or coherent phonons. Other as- pects of Frohlich’s model include metastable states (longer lived conforma- tional state patterns stabilized by local factors) and polarization waves (trav- eling regions of dipole-coupled conformations).

Experimental evidence for such coherent excitations includes observation of gigahertz-range phonons in proteins, sharp-resonant nonthermal effects of microwave irradiation on living cells, gigahertz-induced activation of MT functions in rat brain, and long-range regularities in cytoskeletal structures, such as the superlattice attachment pattern of MAPS on MTs. Figure 2i-t (in the main text) shows that experimentally observed patterns of MAP attach- ment sites on MTs can be simulated and possibly derive from self-localized coherent phonon excitations. Coherent conformational excitations may pro- vide a clocking mechanism for MT information processing in the context of cellular automata.

References

1.

2.

P. Vassilev, M. Kanazirska, and H.T. Tien, “Intermembrane Linkage Mediated by Tubu- lin,’’ Biochemical and Biophysical Research Comm., Vol. 126, No. 1, Jan. 1985, pp. 559- 565.

H. Frohlich, “The Extraordinary Dielectric Properties of Biological Materials and the Ac- tion of Enzymes,” Proc. NatY Academy of Science, Vol. 72, No. 11, Nov. 1975, pp. 4,211-4,215.

November 1992 33

Table 1. Relative net forces for all configurations (= -1,000 y P ) . Net forces are summations of six neighbors.

Central Central Neighbor Dimer a Dimer p Position Neighbor a Neighbor p Neighbor a Neighbor p

North +15.625 +62.500 + 6.944 +15.625 Northeast +15.205 -7.022 + 9.635 +15.205 Southeast -14.250 -8.338 - 7.022 -14.250 South -15.625 -6.944 -62.500 -15.625 Southwest -15.205 -9.635 + 7.022 -15.205 Northwest +14.250 +7.022 + 8.338 +14.250

seven-member MT automata neighbor- hood: a central dimer surrounded by a tilted hexagon of six neighbor dimers. The two monomers of each dimer share a mobile electron oriented either more toward the amonomer (astate) or more toward the p monomer (p state), with associated changes in dimer conforma- tion at each time step.

The net electrostatic force from the six surrounding neighbors acting on a central dimer can then be calculated as

where y , and r, are defined as illustrated in Figure 3b, e is the electron charge, and E is the average protein permittivi- ty. Table 1 shows neighbor electrostatic dipole coupling forces.

To simulate MT automata, we dis- play cylindrical MT structure as two- dimensional rectangles whose edges (ad- jacent protofilaments) are contiguous.

To avoid boundary conditions, end bor- ders also communicate and we model a torus. MT subunit dimer loci are in ei- ther a state (white) or P state (black). At each “nanosecond” time step, we calculate forces exerted by six surround- ing neighbor subunits for each dimer. If the net force exceeds a threshold, a transition (a -+ p, p + a ) occurs. For example, a threshold of f9.0 means that net neighbor forces greater than +9.0 x 2.3 x 10-’4Newton~ (Table 1) will induce an a state, and negative forces of less than -9.0 x 2.3 x Newtons will induce a p state. The threshold may represent temperature, pH, voltage gra- dients, ionic concentration, genetically determined variability in individual dimers, binding of molecules including MAPs or drugs to dimer subunits, and so on.

Figure 4 shows the effects of varying thresholds on MT automata behavior.h Behaviors include gliders (see the “Cel- lular automata” sidebar), traveling and

Figure 4. MT automata models with MTs displayed as rectangular grids.6 Black elements are P-conforma-

tional-state tubulin dimers; white elements are a states. In (a), top: Three successive time steps for four

objects (dot glider, spider glider, triangle glider, and diamond blinker) at threshold f l . O , moving down-

ward, leaving traveling wave patterns; below: Three time steps for a dot glider and three other gliders at a

higher threshold k9.0. The gliders travel downward without a wake. In (b), 10 successive time steps of MT automata with asymmetrical thresholds: a to p thresh- old is -20.0; p to CI threshold is +2.0. The initial condi- tions (not shown) were a seeds on p background. A p

bus glider (black kinky pattern) moves upward as a new a glider (white line) moves downward.

standing wave patterns, oscillators, lin- early growing patterns, and frozen pat- terns (perhaps suitable for memory). Asymmetrical thresholds ( a + P f p -+ a ) result in bidirectional gliders (Figure 4b).

Assuming MT conformational autom- ata gliders and patterns exist, what func- tions could they have? They could rep- resent information being signaled through the cell. Glider numericalquan- tities and patterns may manifest signals, binding sites for ligands, MAPs, or ma- terial to be transported. Frozen pat- terns may store information in a memo- ry context, information may become “hardened” in MTs by posttranslation- al modifications, or MT automata pat- terns could transfer and retrieve stored information to and from neurofilaments via MAPs.

MT automata gliders travel one dimer length (8 nm) per time step to to-” second) for a velocity range of 8 to 800 meters per second, consistent with propagating solitons or phonons as well as nerve membrane potentials. Thus, traveling MT automata patterns or glid- ers (equivalent to solitons, phonons, or Frohlich depolarization waves) may propagate in the cytoskeleton in con- cert with membrane depolarizations and ion fluxes. Long-range cooperativity, resonances, and phase transitions among spatially arrayed MTautomata patterns may occur, and membrane-related volt- ages, ion fluxes, or direct links could induce transient waves of conformation- al switching or lowered threshold along parallel-arrayed MTs. Consequently, activity of a particular cell could direct-

34 COMPUTER

ly elaborate patterns within that cell’s MT automata - phenomena important in emergent cognitive and behavioral functions ranging from relatively sim- ple organisms to complex human brains.

MT-MAP network formation. Cell architecture and functions depend heavi- ly on cytoskeletal lattices, consisting largely of MT-MAP networks. MAPS stabilize MTs, preventing disassembly and promoting assembly. We investi- gated MT stabilization by MAP binding on adjacent. parallel MTs as an initial step in construction of an MT-MAP network.

We assume periodic distributions of MAP attachments on MTs (see Figure 5a) and that MAP binding to a specific tubulin increases its affinity to its six surrounding neighbors. This neighbor- hood then becomes resistant to disas- sembly’ (Figure 5b). Maintaining a pe- riodic distribution of MAPs, only afinite number of MAP attachment sites are available for each rcgion on an MT. The number of MAPs per region and their particular location(s) within that region may be related to the reduction of the free-energy value that, in turn, may be related to the stabilization of MTsubas- semblies. On the basis of a “mobile finite automata” technique, Figure Sc shows a number of MAP distributions and their calculated free-energy values. The efficiency in free-energy reduction depends on and determines both MAP location and number.

Learning via optimization of MAP connection sites. We next consider adap- tive behavior in simple MT-MAP au- tomata networks demonstrating IiO learning found in artificial neural net- works. Two MT automata are intercon- nected via MAP connections capable of signal transmission (sequences of a or p conformational states) from one MT to another. MAP connection sites vary randomly in an evolutionary optimiza- tion process, and we define two inputs and one output as regions on the two MTs (Figure 6). For two different sets of MT1 and MT2 input pairs (automata patterns), we predefine a desired or correct output pattern. After each se- quence of time steps (sufficient for pat- terns to propagate from the input areas to the output area, with transmission across MAP connections), we compare the output area pattern with the desired output pattern using a mathematical

Figure 5. Simulation of MAP connections and MT network initiation: (a) some possible MAP connection sites and connection topologies; (b) MT disassembly until stabilized by MAPs; (c) MT-MAP quantity and connection topologies which promote neighbor M T assembly and stability. Three possible “rows” of MAP connection sites are considered; negative free-energy values were calcu- lated and are shown in rectangles.

I Lehming

Figure 6. Schematic drawing of an MT network (a). Two MT automata (MTA1 and MTA2) of length I = 80 dimers are interconnected by a MAP automaton (MAPA,). Two input areas, Z, and Z,, are defined at the right end of each MTA, and one output area, (O,), at the left of MTA2. MAPA, transmits dimer states from its input area inpj in MTAl to output area oupi in MTA2. In (b), for each pair of input patterns ZI1, Z,, or I , , , I,, there exist desired output patterns O,,* or 0,; on MTA2. In (c), input I , , and Z,, with desired output O,,*. In (d), I,, and Z,, with desired output 0,;.

formulation of error called the Ham- ming distance. The Hamming distance, or H,, is the number of digit positions in which two binary words of the same length differ. Allowing random MAP connection topologies between the two

MTs, we select the most efficient topol- ogy (that which yields the lowest Ham- ming distance) as the “mother system” after each time-step sequence. At the next step, other “daughter” topologies are randomly created. Whenone daugh-

November 1992 35

Figure 7. MTA net learning process (a). The connec- tion topology with MAPs at dimer lo- cations MTAl (60,6) -+ MTA2 (55,2) and M T A l (47,4)+ MTA2 (41,3) satisfies the first U 0 map with H, = 0. From top to bottom, dynam- ics are shown at time steps 0,43, and 66. The same MT net at a later stage of the learn- ing process (b). The topology with MAPs at dimer locations is the same as in (a) but with an additional MTAl (28,7) + MTA2 (29,5), which satisfies both IIO maps with H, = 0. Dynamics are shown at time steps 0,26, and 66 after the third MAP. Thresholds for M T A l and MTA2 were k5.9 and k9.0, respectively.

ter performs better than the original system (lower Hamming distance), this connection topology becomes the moth- er system for the next generation.h

Figures 6c and 6d show U0 maps ( I , , , lzl) + 0,, and ( I , , , 12J -+ 022 used for learning trials. Figure 7a shows the con- nection topology C, + C, that satisfies the first 110 map, together with the net- work patterns at times 0.43, and 66 ( H , = 0). Figure 7b shows the connection

topology C, + C, that satisfies the sec- ond I/O map, together with correspond- ing MT patterns at times 0, 26, and 66 ( H d = 0). This topology also satisfies the first U0 map. Because of perturbation- stable glider patterns, the MT network can also “associate” patterns - that is, produce correct outputs from inputs which are similar, but not identical, to the original output-coupledinputs (Fig- ure 8).

Figure 8. Association of patterns in an MT net with the connection topology shown in Figure 7. Parts (a) and (b) are related to the first trial sequence, and (c) and (d) to the second. In (a), H, = 26, (b) H , = 6, and (c) H , = 0. Thus the network can “associate” similar patterns.

Membrane-coupled MT-MAP recog- nition. This model system considers MAPs attached at fixed loci between two MT automata as switches (“open” or “closed”). Each MAP’S state (open or closed) is determined by membrane receptor activation (that is, by binding of neurotransmit ter molecules t o postsynaptic neuronal receptors) cou- pled to the MAPs by second messengers (for example, G proteins, [Ca++], cyclic adenosine monophosphate (cyclic AMP), protein kinases, MAP phospho- rylation). In neurons and other cells, second messengers connect membrane events to internal functions, including gene regulation and cytoskeletal activ- ities. Figure 9 shows three binary recep- tor inputs, modeling the binding (1) or lack of binding (0) of neurotransmitter molecules. Receptors regulate MAP1 and MAP2, which each interconnect MT1 and MT2. If either MT1-MAP con- nection tubulin is in a state and the MAP is open, the corresponding MT2- MAP connection site will be perturbed (if a, then p; if p, then a). MAPs have a critical phosphorylation threshold, above which MAPs are “open.” Out- puts occur on MT2 distal to both MAP attachments.

We used this model network in the training and recognition exercise illus- trated in Figures 10 and 11. As an arbi- trary example, we expressed character- istics of virus structure in three binary categories as inputs to the receptors. We categorized four types of viruses - microvirus, papovavirus, adenovirus, and herpes virus - by three character- istics:

(1) Virus coat: naked = 1, enveloped = 0 (Figure loa).

(2) Number of capsomer subunits in protein capsids: less than or equal to 32 = 1, more than or equal to 72 = 0 (Figure 10b).

(3) Diameter of virus (in nanome- ters): less than or equal to 50 = 1, more than 50 = 0 (Figure 1Oc).

Figure 10d shows results of a virus rec- ognition test. Figure 11 shows training sets and MT2 automata outputs for the four virus patterns. The virus recogni- tion test correctly identified five of six viruses.

Artificial neural network models. Artificial neural networks are comput- er designs for learning and computation

36 COMPUTER

ackward propagation

MAP threshold

+ MT automata (Output)

11001 01001 1101 1000000101000100 100101010001010010010100010100

I

Figure 9. Schematic drawing of a receptor-coupled MT network model. Three “receptor” inputs have two possi- ble states related to neurotransmitter binding (occupied = 1, unoccupied = 0). These regulate “second messenger” systems, viewed as variable-weight connections, which phosphorylate two MAPs that interconnect two MT au- tomata. Above a critical threshold of receptor-triggered second messenger activity, the MAPs are open. On MT1- MAP connection sites, a states change states on corre- sponding MT2-MAP connection sites. Feedback from MAP states regulates weights of receptor-MAP connec- tions. Output occurs on MT2.

Micro - Pap0 Adeno

(a)

I Enveloped *

I l l 1 550 A A >50 G O >50

- - - Herpes

I 1

I 0

1 A A A & 0 1 0 1 0 0

1 1 1 1 1 1 1 1 111 110 101 100 011 010 001 000

Input MAP1 MAP2 Virus group

1 Microviridae 111 1 101 1 0 Papovaviridae

1 Adenoviridae 100 0 000 0 0 Herpesviridae

Micro Pap0 Adeno Herpes

- - Micro 1 - - I Probability (+)=5/6 Probability (-)=I16 Adeno

Herpes

+ Right classification - Error classification

(d)

a b c d

Adenoviridae Microviridae Papovaviridae Herpesviridae

Figure 10. Binary coding of virus char- acteristics for the MT network (a-c). Test results (d): Five out of six identi- fications were correct.

Figure 11. Temporal evolution of MT automata patterns at 2,4,6, and 8 time steps with MT2 automata pat- terns for four viruses s tudied (a) MAP left closed, MAP right open; (b) MAP left open, MAP right closed; (c) both MAPS closed; (d) both MAPs open.

November 1992 37

Nuclet

terminal

Figure 12. Model of back-propagation learning in a biological neuron. Delta (6) “error” signals propagate within MTs along axon branches to the axon trunk (in a direction opposite to membrane depolarization). The 6 signals are aver- aged and transmitted (s) along dendritic trunks, where they adjust synaptic strengths.

based on processing units inspired by biological neurons. Although some ar- tificial neural network activities seem biologically plausible, those that require backward feedback along each forward connection have not appeared biologi- cally plausible without retrograde in- ternal signals within neurons (axon to dendrite). Artificial neural network paradigms that use backward feedback include back-error propagation, sigma- pi and restricted coulomb energy (RCE) architectures, and adaptive resonance theory. Backward feedback across syn- apses in biological neurons has now been shown likely to occur via nitric oxide. Backward neuronal feedback signals, if provided by membrane potentials, would require each forward connection to have a complementary backward neuronal synaptic connection. If provided by ret- rograde axoplasmic transport, backward feedback signals would be rather slow.

The cytoskeleton may be capable of carrying fast conformational feedback signals backward through a network of neurons. Figure 12 shows a schematic neuron with its internal cytoskeleton. Axonal branches (on the right) convey error signals d(Riarge,-Rourpui) back to the axon hillock, where they are averaged and transmitted to dendritic synapses to adjust synaptic strengths (s) accord- ingly. The strength of the backward sig- nal (for example, automata gliders) could be in the number of gliders or in the size of the MT bundle that carries that sig- nal. To modulate feedback and mediate learning, bundles might grow, shrink, and change stability via pattern-induced

MAP binding, nucleationistabilization of adjacent MTs, posttranslational mod- ifications. and so on).

onformational automata in the cytoskeleton could process in- formation in living cells and pro-

vide a molecular substrate for cognitive functions. Thus, we portray the cytoskel- eton as the cell’s nervous system, with microtubules serving as processors or signal carriers and MAPs as molecular cross-bridge connections (“synapses”). In the brain, each neuron’s cytoskele- ton could be viewed as a “fractal-like” subdimension in a hierarchy of adap- tive networks.

We have explored only a few facets of the possible parameter space for MT- MAP information processing: subunit coupling strength (threshold), initial conformational patterns (to a limited extent), MAP attachment sites, and MAP transmission between two MTs. Other possible parameters include MAP quantity and variety; whether MAPs attach to MTs in series or in parallel (for example, along the same protofilament or different protofilaments within a giv- en MT): clocking frequency and degree of coherence; quantity and genetic het- erogeneity of MTs, neurofilaments, and other cytoskeletal structures; ligand binding; resonances; phase transitions; “coded” MAPs; and MAP attachment sites determined by MT free-energy minimization, phonon maxima, or spe- cific automata patterns.

Cytoskeletal conformational autom-

ata imply an enormous information pro- cessing capacity. For example, the infor- mation processing capacity of a human brain, based on consideration of con- ventional neural synaptic transmissions as fundamental switches, can be esti- mated as 100 billion neurons, each with more than 1,000 synapses “switching” 100 times per second to yield at least 1016 “bits” per second. Considering the sim- plest case of cytoskeletal conformation- al automata (two conformational states per MT subunit switching at 1 0-9-second intervals, lo4 MT subunits per neuron) yields about lo?? brain bits per second, permitting ample parallel redundancy. To this we may add (or multiply) tubulin heterogeneity, variability of MAPs, neu- rofilaments, resonances, phase transi- tions, and quantum effects. To examine the possible involvement of cytoskele- tal structures in cognitive processes. tech- nologies will need to approach the nanoscale (nanometer size, nanosecond time). As electrophysiological record- ing revealed neuronal membrane dy- namics, emerging nanotechnologies in- cluding scanning-tunneling and atomic-force microscopies will be need- ed to investigate cytoskeletal dynamics.

Tubulin may be isolated and mass- produced by genetic engineering tech- niques. Under proper conditions, itself- assembles into MTs or flat lattice sheets. If computation occurs in MTs and can be decoded and accessed, cytoskeletal arrays may provide “devices” with sub- stantial computing power. Perhaps such systems will someday reach cognitive capabilities comparable to and even su- perior to human abilities. At least the cytoskeletal arrays would provide a unique approach for computing on the nanoscale, with components both faster and smaller than components on cur- rent devices.

While the ideas of dynamic coding and technological intervention in the cytoskeleton may seem farfetched, are they any more radical than were the ideas of static genetic coding and inter- vention in DNA (deoxyribonucleic acid) and RNA (ribonucleic acid) some years ago? We hope to provoke exploration of molecular information processing in cy- toskeletal assemblies. W

Acknowledgments Stuart R. Hameroff (partially) and Alexei

V. Samsonovich are supported by NSF Grant

38 COMPUTER

No. DMS-9114503. Judith E. Dayhoff is sup- ported by the Naval Surface Warfare Cen- ter, Dahlgren, Virginia, and the Institute for Systems Research, University of Maryland. Rafael Lahoz-Beltra is supported by Minis- terio de Educacion y Ciencia in Spain under FulbrightiMEC (1989-1991) and FPIiMEC (199 1-1992) grants.

The authors thank Michael Rush for tech- nical support, and Alwyn Scott and Djuro Koruga for scientific advice.

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2.

3.

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N. Hirokawa, “Molecular Architecture and Dynamics of the Neuronal Cytoskel- eton,” in The Neuronal Cytoskeleton, R.D. Burgoyne. ed., Wiley Liss. New York, 1991. pp. 5-74.

P. Dustin, Microtubules. 2nd ed., Spring- er-Verlag. Berlin, 1984.

S.R. Hameroff. UltimateComputing: Bio- molecular Consciousness and Nanotech- nology, Elsevier-North Holland, Amster- dam. 1987.

L.A. Amos and A. Klug, “Arrangement of Subunits in Flagellar Microtubules,” .I. Cell Science. Vol. 14, No. 3, May 1974. pp. 523-550.

M. De Brabander, “A Model for the Mi- crotubule Organizing Activity of the Centrosomes and Kinetochores in Mam- malian Cells.” Cell Biology Inr’l Reports. Vol. 6, No. 10, Oct. 1082. pp. 901-915.

6. S. Rasmussen et al., “Computational Connectionism Within Neurons: A Mod- el of Cytoskeletal Automata Subserving Neural Networks,” Physica D , Vol. 42, Nos. 1-3, June 1990, pp. 428-449.

7. H. Hotani et al., “Microtubule Dynam- ics, Liposomes and Artificial Cells: In Vitro Observation and Cellular Autom- ata Simulation of Microtubule Assem- blyiDisassembly and Membrane Morpho- genesis,”Nanobiology,Vol. 1,No. I, 1992, pp. 61-74.

Stuart R. Hameroff is an associate professor in the Department of Anesthesiology in the University of Arizona Health Sciences Cen- ter in Tucson. where he divides his time among clinical anesthesiology. teaching. and research. His research interests include mo- lecular mechanisms of anesthesia and con-

sciousness, scanning-tunneling microscopy, neural networks, and the cytoskeleton. He has published more than 80 papers, and writ- ten Ultimate Computing: Biomolecular Con- sciousness and Nanotechnology (Elsevier- North Holland, 1987). He organized the 1991 NATO Advanced Research Workshop on Coherent and Emergent Phenomena in Bio- molecular Systems, and is North American founding editor of the new journal Nanobi- ology (Carfax Publishing).

Hameroff received his BS in chemistry from the University of Pittsburgh in 1969 and his MD from Hahnemann Medical Col- lege in 1973. He completed his anesthesiolo- gy training at the University of Arizona in 1977, and became a diplomate of the Amer- ican Board of Anesthesiology in 1979.

Judith E. Daghoff is a member of the faculty at the Institute for Systems Research at the University of Maryland and is a visiting fac- ulty member at the Naval Surface Warfare Center, Dahlgren, Virginia. She has per- formed research in biological and artificial neural networks, developed models of cy- toskeletal participation in neuronal plas- ticity and learning, and identified architec- tures for biomolecular computers. She authored Neural Network Architectures: A n Introduction (Van Nostrand Reinhold 1990) and is on the Governing Board of the Inter- national Neural Network Society.

Dayhoffreceived her BA inchemistry from Duke Univcrsity in 1975 and her PhD in biophysics from the University of Pennsyl- vania in 1980.

Rafael Lahoz-Beltra is an associate proles- sor in the Department of Applied Mathc- matics, Faculty of Biological Sciences. Com- plutense University of Madrid. He was a Fulbright Visiting Research Scholar in the Department of Systems Science, T.J. Wat- son School of Engineering, State University of New York at Binghamton. from 1989 to 1990, and continued his work under his Ful- bright Scholarship from 1990 to 1992 at the University of Arizona. His main research

interests are cellular automata, the origin of life. synaptic regulation, and microtubule in- formation processing.

Lahoz-Beltra earned his BS in biological science in 1985 and his PhD in biostatistics in 1989 from the Complutense University of Madrid.

Alexei V. Samsonovich is a PhD student in applied mathematics at the University of Ar- izona, where he is studying quantum self- trapping under a National Science Founda- tion grant. His recent research work has focused on acousto-conformational phase transitions in the cytoskeleton. His long-term goals include molecular electronics, quantum computing, and human brain interfacing.

Samsonovich was awarded a Golden Med- al at the Kiev (Russia) Physical Mathemati- cal School in I974 and a diploma on the theory of parity violation by weak atomic interactions at the Moscow Physical Techni- cal Institute.

Steen Rasmussen has been a staff researcher at the Center for Nonlinear Studies and The- oretical Division at the Los Alamos National Laboratory since 1988 and at the Santa Fe Institute since 1991. He is a primary figure in the artificial life movement, initiated bio- chemical experiments in the origin of life, studied self-organization in computers. and modeled learning and adaptive behavior in cytoskeletal microtubules. He co-organized the NATO Advanced Research Workshop on Coherent and Emcrgent Phenomena in Biomolecular Systems at the University of Arizona in 1991, and is a founding associate editor of Nunobiology (Carfax Publishing).

Rasmussen earned his master’s degree in dynamical systems in 1982 and his PhD in physics in 1986. both from the Technical University of Denmark.

Readers can contact Hameroff at the De- partment of Anesthesiology, University of Arizona Health Sciences Center, Tucson, AZ 85724, e-mail stuartmt@ccit.arizona.edu.

November 1992 39