Michael Conrad and Klaus-Peter Zauner- Molecular Computing with Artificial Neurons

Not for generaldistrib ution; prepublicationprint of materialto appearin J.KoreanInformationScienceSociety. 1

Molecular Computing with Artificial NeuronsMichael Conrad and Klaus-Peter Zauner

Departmentof ComputerScienceWayneStateUniversity

Detroit,MI 48202,U.S.A.e-mail: [email protected]

Abstract—Today’s computers are built up from aminimal set of standard pattern recognition opera-tions. Logic gates,such as NAND, are common ex-amples. Biomolecular materials offer an alternativeapproach,both in terms of variety and contextsensi-tivity. Enzymes,the basicswitching elementsin bio-logical cells,are notable for their ability to discrimi-natespecificmoleculesin a complexbackground andto do soin a manner that is sensitive to particular mi-lieu featuresand indiffer ent to others. The enzyme,in effect, is a powerful context sensitive pattern rec-ognizer. We describe a tabletop pattern processorthat in a rough way can be analogizedto a neuronwhoseinput-output behavior is controlled by enzy-matic dynamics.

Keywords artificial neuralnetworks, patternrecogni-tion, biological informationprocessing,enzymekinet-ics,signalprocessing

1 Neuronal Pattern Processing

In 1904 a school teacherfound that he was able tosuccessfullyteachhis horse,Clever Hans,elementarymathematics.If heaskedHansfor thesumof two dig-its, thehorsewould tapout thecorrectresult. It turnedout,however, thatthehorsewasnotdoingarithmetic.Itusedminute involuntary reactionsof its teacherto de-cidewhento stoptapping(O’Gradyetal. 1997,p. 612).At the time, thesummaryjudgmentwasthatHanswasnot at all clever. But just try to programa computertoperceive andlearnhow to utilize subtlechangesin ex-pression.Fromtheviewpoint of today’s computertech-nology addingthe digits seemstrivial comparedto thepatternrecognitionproblemthehorsechoseto solve.

Theeloquencewith whichbiologicalorganismshan-dle patternprocessingtaskscan be tracedto molecu-lar patternrecognitioncapabilitiesof macromolecules

(Conrad1992).Proteinsareparticularlyversatilein thisrespect. Proteincatalysts,or enzymes,arecapableofdiscriminatingandactingon specificmolecularshapesin a complex milieu and doing so in a mannerthat isselectively sensitive to themilieu context.

Towhatextentdoesthisintrinsiccapabilityof macro-moleculespercolateup into theperception-actioncapa-bilities of aCleverHans?Thequestionclearlyhasmuchto do with the capabilitiesof neurons.Is the neuronameresummatorof its inputs, reactingonly to an aver-agefield, or is it itself a powerful molecularcomputer?Oneof thegreatpioneersof neuralcomputing,WarrenMcCulloch,madeacommentpertinentto thispoint:

“For our purposeof proving thata realner-vous systemcould computeany numberthata Turing machinecould computewith a fixedlengthof tape,it waspossibleto treattheneuronasa simple thresholdelement. Unfortunately,thismisledmany into thetrapof supposingthatthresholdlogicwasall onecouldobtainin hard-wareor software. This is false.A realneuron,or Crane’sneuristor, cancertainlycomputeanyBoolian [sic] functionof its inputs—tosaytheleast!” (McCulloch1965,pp. 393,394)

To this it is perhapsworth addingthat in the cerebralcortex of the mouse,for example,the averagenumberof synapses(inputs)perneuronis 8000(Schuz1995).Itis awkwardevento think of Booleanlogic in thefaceofsuchhigh connectivity.

Wecannoteanotherbit of history, connectedwith theperceptronconceptof Rosenblatt(1962). This conceptindeedusedanessentiallythresholdneuron.Rosenblattfoundasimple,effective learningalgorithmfor asinglelayer perceptron. The idea was severely criticized byMinsky andPapert(1969). Thesinglelayerperceptroncould not be usedto discriminatelinearly inseparablepatterns.Theexclusive-or (XOR) operationis thesim-plestexample.Multilayer perceptronscanof coursedo


this job, ascanlaboratoryrats(Griffith etal. 1968).Butthenthedefinitelearningalgorithmusedby Rosenblattno longer applied. Evolutionary methodsof learningcould be employed. However, for variousreasonsthecomputersciencecommunityat the time wasnot pre-paredto acceptself-organizingsystemsandevolution-ary methods.Handcraftedapproachesweretheorderoftheday. Neuralnetsandevolutionaryapproacheshadtosit on thesidelinesuntil relatively recently.

Thereis anotherwayoutof theXOR limitation. Theneuron,asnotedby McCulloch, neednot be a simplethresholdelement. We will show herethat individualenzymescan be usedto perform the XOR operation.Neuronsandotherbiologicalcellscontainthousandsofinterlinked enzymes.Our assumptionis that theoppor-tunity seekingprocessof evolution usestheseenzymenetworks to implementcomplex information process-ing functionsat the cellular level. We have developeda tabletopprototype,a crudeartificial neuronof sorts,thatmakesit possibleto investigatehow suchmolecularpatternrecognizerscouldbeutilized in adevicecontext.Conceivably thepatternrecognitionvirtuosityof naturalbiologicalcellsis basedonsimilar operative principles.

2 EnzymeBasics

Enzymesare proteinsthat act as highly specificcata-lysts capableof discriminatingparticularsubstratesina complex chemicalbackground. The catalytic func-tion performedis controlledby the enzyme’s shape—its 3-D spatialstructure(Friedrich 1984). This struc-tureis largely determinedby aminoacidsequence.Thestructureis not rigid; it undergoesconsiderablecon-formationalmotion, i.e., rotationaroundatomicbonds(Frauenfelderet al. 1988; Yon et al. 1998). Whichsubsetof conformationalstatesis favoredis a functionof anenzyme’s physiochemicalenvironment.Catalyticactivity is critically dependenton conformationalstateandthereforeprovidesa sensitive andconvenientprobefor conformationchange.The intricateconformationaldynamicsof the enzymefusessignalsfrom its physio-chemicalmilieu andmodulatescatalyticactivity. Theenzymeis in effectanimplementationof a functionthatmapsnumerousselectedvariablespresentedasphysio-chemicalcontext into outputcommunicatedascatalyticactivity.

The cell, asnotedearlier, containsthousandsof en-zymes. In single celled organisms,such as amoebaor paramecium,all the information processingis me-diatedby theinternalmolecularnetwork. Chemicalsig-nals from the environmentare communicatedthroughthe cell membrane,eitherdirectly or by triggering thereleaseof internal chemicalsthrough interactionwithmembranereceptors(seeFig. 1). The signalsinflu-

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Figure 1: Conformational signal processing in bi-ological cells. Impinging chemical signals directlyor indirectly affect the internal milieu of the cell.The conformational dynamics of proteins and othermacromolecules is selectively sensitive to thesemilieu features. These nonlinear dynamics in ef-fect process the milieu influences to yield internalor external cellular actions.

encethe conformationaldynamicsof specificenzymesin thesenetworks, leadingto cascadesof reactionsthateventuallyculminatein the actionof the cell. In neu-rons,for example,transmittersimpinging on theexter-nal membranemay be transducedto cyclic nucleotidemoleculeswithin the neuronthat serve assecondmes-sengers.Thesecanaffect target proteinson DNA, onthe various internal fibrous structuresof the cell (thecytoskeleton)or on themembrane.The target proteinsthenactivateeffector proteins;for example,membranechannelproteinsthat control the nerve impulse(Liber-


manet al. 1975).

Thecell in Fig. 1 is schematicallypicturedasa kindof mixing chamber. In fact the interior of the cells ofhigherorganismsis highly structured,with many fibersandmembranousinterfaces.Thefibers,asnotedabove,are referredto as the cytoskeleton, sincethey are re-sponsiblefor maintainingthestructureof thecell. Theyaresometimesthoughtof as micro-muscle,sincetheycontribute significantly to cellular motionsand to themovementof materialswithin the cell. Somelines ofevidencesuggestthat thecytoskeletalfibersalsoactasa kind of micronervous systemwithin cells and neu-ronsthatservesto coordinateinternalactivities (like thehighly choreographedprocessof cell division)andplau-sibly to mediatemoresubtleformsof signalprocessingpertinentto the cell’s capabilityof integratingexternalsignalsin spaceandtime (MatsumotoandSakai1979;Libermanet al. 1985;Hameroff 1987).

The tabletopdevice to be describedis a highly ab-stractedversionof thiscomplex intracellularprocessing.Threebasicelementsenterinto this abstraction.Macrosignalsmustbetransducedto a form thataffectstheac-tivity of an enzymeor a collection of enzymes. Theactionof the enzymemustnot be confinedto an aver-aging processthat could be performedby a transistor(e.g., OR, AND, NAND). If this were the caseall ofthepowerful shape-basedrecognitionactivity of theen-zymewouldbelost. Programmabilityshouldnotbeim-posedsincethis requireseachcomponentto haveacon-text independentdescriptionthat would vitiate the dis-tinctiveadvantageof enzyme-drivencomputing,namelythe possibility of utilizing the vastnumberof potentialinteractionsin multiplewaysfor multiplepurposes.Thekey to the power of the systemis self-organizingdy-namicsat the level of the enzymeand at the level ofmacromolecularnetworks. If the systemcould be pro-grammedprescriptively, like a digital machine,thenallthepowerof thisself-organizationwouldhaveto besup-pressed.Self-organizingsystemsafterall haveamindoftheir own. Evolutionaryadaptive approachesarecalledfor (Conrad1985;1990).

3 The TabletopNeuron

We constructeda tabletopprototypethat usesthe en-zyme malatedehydrogenase(MDH) to classify inputsignalpatterns.MDH occursin awidevarietyof speciesincluding themicrobialworld andin plants. In our ex-perimentswe usedmitochondrialMDH from pig heart,a homodimerwith each monomerconsistingof 314aminoacids(Gleasonet al. 1994).

MDH catalyzesthe oxidation of malateto oxalac-etateby reducingtheoxidizedform (NAD ' ) of nicoti-namideadeninedinucleotide(NAD) to thereducedformNADH.

L-malate(*),+�- '.0/�123

oxalacetate(4)�+,-654(45 'NADH differs significantly from NAD ' in its absorp-tion of ultraviolet light. This propertyof the reactionproductmakes it convenientto monitor the activity ofmalatedehydrogenaseby spectrophotometricmethods.

For high pH theequilibriumof thereactionis on theright side.Thetimecourseof thereactionis affectedbythe sensitivity of the enzymeto chemicalcontext, i.e.,the milieu in which the reactiontakes place. The mi-lieu is composedfrom a numberof fixed components,suchas the substratesandpH buffer, plus the compo-nentsrepresentingthesignals.In theexperimentsto bedescribedhereMgCl 7 was usedas the signalingsub-stance.Similareffectscanalsobeachievedwith CaCl7 ,but themethodis not restrictedto ionsor to any definitenumberof signalcarriers.

Thedeviceitself is schematicallyillustratedin Fig.2.Signalsare injectedinto a mixing chamberin two 1

ml portions,taken in any of four possiblecombinationsfrom thetwo signalingsolutions.Solutionsrepresenting0 and1 containsubstratein thesamequantity, but the1-solutionin additioncontainssignalingions. Thequan-tity of MgCl 7 representinga 1-signalis chosenso thattheabsorbanceresultingfrom asingledoseof signalingsubstanceis maximally separatedfrom the absorbanceproducedeitherby adoubledoseor nodose(whicheveris closer).Thereactionmixture(a fluid phasetravelingin an air-filled tubing, Fig. 3) is pumpedto the spec-trophotometer. The accumulationof NADH serves asoutputsignal.After processingis completedthesystemis clearedfor thenext inputpatternby pumpingdistilled


Mixingchamber

Spectrophotometer

Peristaltic pump

1-Signal,Substrate

0-Signal,Substrate

Enzyme

H2O forclearing

R1

R2

R4

R3

S1 S2

S3 S4

S5

V1 V2

V3 V4

V5 V6

atm V7 T1

T2T3

atmT4

T5

T6atm

atm

11

0 0

atm

Figure 2: Flow system used in the XOR experi-ments. Signals are injected from any two of four sy-ringes (S1 to S4). The 1-syringes (S1 and S2) arefilled from reservoir R1 that contains signal sub-stance (Mg 7 ' ) plus substrate. R2, the reservoirfor the 0-syringes (S3 and S4), contains substratein the same concentration as R1 but no signalingsubstance. Signals are injected through valves (la-beled by V) into the mixing chamber. Enzyme so-lution (MDH and NAD ' in buffer) is stored in thethermally isolated reservoir R3. The reaction is ini-tiated by injecting this solution, using syringe S5,into the mixing chamber. The reaction mixture isdrawn by a peristaltic pump into a flow cuvette in-stalled in the spectrophotometer. The absorbanceof the product NADH at 339 nm serves as outputsignal. Reservoir R4 contains distilled water whichis used to wash the system clean after the inputpattern is processed. T valves (T1 to T6) are usedto switch from processing to clearing. Tubes la-beled atm (atmosphere) are air in/outlets.

waterthroughit. Theoutputsignalis sentto acomputer.If thesignalis above a singleprescribedthresholdlevela 1 is displayed,otherwisea 0. Several trials are runto calibratethe threshold. When the reactionmixturereachesthe cuvette the absorbanceincreases.This in-creaseis usedto trigger a countdown to a subsequentabsorptionmeasurementthat decidesthe output. Theactualimplementationis picturedin Fig. 4.

8:9 ;

<>=@?BA�CD9 E@FHGI=�JK9 LNM

Figure 3: Two phase transport utilized in the table-top implementation. The reaction medium (fluidphase) travels in air-filled (gas-phase) tubing fromthe mixing chamber to the detector.

Figure 4: Laboratory setup used to implement the arti-ficial neuron.

4 Enzymatic Pattern Classification

TheXOR operationrequiresa device to sayyes(give a1 output)in responseto binarysignalinputs01 and10andto sayno (give a 0 output)to 00 and11 input pat-terns.Theoperationis linearly inseparable,correspond-ing to thefactthatthepatternstobeplacedin theyesandno categoriescannotbeseparatedby a singlethreshold(in contrastto NAND, AND andOR operations).Anelementwhoseresponseis linear apart from a singlethresholdcannotperform the XOR, sinceit would benecessaryfor it tofire whenthestrengthof thecombinedinput exceedsa lower thresholdandnot fire whenit ex-


ceedsa higherthreshold.If theresponseof theelementis nonlinear(strictly speakingnonmonotonic)thenit ispossibleto eliminatethe needfor the higher thresholdandthereforeto convert thelinearly inseparablepatternrecognitionproblemto a linearly separableproblem.

An enzyme,to satisfythisrequirement,mustincreaseits activity in responseto onedoseof thesignalingsub-stancebut decreaseit in responseto two doses. Wefound that MDH satisfiesthe requirementwith respectto MgCl 7 usedas a signalingsubstance.Thus whenMDH is usedastheenzymein themixing chamberthedeviceyieldsa0 outputwhentheinput is 00,a1 outputwhentheinputis 10or 01,anda0 outputwhentheinputis 11.

Fig. 5 illustratesa seriesof 42 XOR tests,with thetrigger set for an average10 secondresponse. Thethresholdwassetbasedon thefirst measurementof thethreedistinguishableinputpatterns(since01is thesameas10). Only one input patternwas incorrectly classi-fied. It is possibleto choosea thresholdthat separatesthecasesmoresecurely(but all settingswould leave atleastonefailure in this series).Tensecondsis nearthelimit of thedevice in its presentform, duein partto thetypeof pumpandspectrophotometeremployed.There-actionthatdrivesthedeviceis theonly fundamentallim-iting factor. This canbespedup by increasingthecon-centrationof enzymeor by warmingthe reactionfluid.The importantpoint is thatMDH servesasa transformthat convertsa linearly inseparablepatternrecognitiontaskinto a linearly separableone.

5 Temporal Signal Processing

TheXOR operationwasimplementedby takingasnap-shotof the responseof our tabletopneuronat a partic-ular point in time asoutputvalue. The chemicallyen-codedsignalswerepresentat the startof the reaction.Thecourseof thereactionwasdeterminedby theinitialreactionconditions. Reducingthe amountof enzymeslows the reactiondown. Its progresscanthenconve-niently be followed andis shown in Fig. 6 for variousamountsof MgCl 7 . As canbe seenfrom the crossingcurvesin Fig. 6, achangein MgCl 7 concentrationhasaqualitative effecton thecourseof thereaction.

Toutilize thephenomenologicalenzymebehavior we

0-0 0-1/1-0 1-1

0.2

0.4

0.6

0.8

1 T

Input aInput b

00

01

10

or11

A

0.8

0.6

0.4

0.2

1.0

0

Figure 5: Pattern grouping with MDH as illustratedby XOR task. The three distinguishable input pat-terns are grouped into two output categories de-pending on whether the amount of product formedis above or below the threshold (T). The time whenmeasurements used for classification are taken iscontrolled by a trigger mechanism. The times fallbetween 9 and 11 seconds after start of the reac-tion, with two exceptions. The last measurement inthe 00 and also the 11 pattern sets were triggeredearly, leading to low absorbance values (denotedby A). The 10 second absorbance values recordedwere below the threshold and hence would stillhave been correctly classified. A 0-signal is rep-resented by 1 ml of 7.1 mM malate and 112 mMglycine. A 1-signal is represented by 1 ml of 190mM MgCl 7 , 7.1 mM malate, and 112 mM glycine.Both signal solutions are adjusted to pH 10.5 withNaOH. Two ml of input signal solution constitute aninput pattern. The reaction is initiated when thiscombines with 1 ml of MDH-NAD ' solution (5.3mM NAD ' in MOPS buffer adjusted to pH 7.4 withNaOH).

needto decideon anencodingfor thesignalpatternstobe processed.A simpleencodingschemerepresentsa1-signalarriving on a signal line by a fixed amountofonesubstanceanda0-signalby theabsenceof thissub-stance.Suchanencodingallows for theimplementationof commutative operations( OQP�RTSUR�P�O ) only, sincea changein the order of the operandswill not lead toa changein the chemicalmilieu. Therefore2-bit inputpatternswill give rise to 3 possiblemilieu states,here


Absorbance (339 nm)

t [s]

MgCl2none

16.7 mM

33.3 mM

66.7 mM

100 mM

133.3 mM

500 1000 1500 2000 2500 3000 3500 4000

0.5

1

1.5

2

2.5

Figure 6: Measured absorbance change overtime for various Mg 7 ' concentrations. The re-action medium contained 4.8 mM L-malic acid,1.8 mM NAD ' , and 13.2 mM MOPS (3-[N-morpholino]propanesulfonic acid, used to bufferthe enzyme (porcine heart mitochondrial MDH)and NAD ' solutions) and was buffered by 92 mMglycine adjusted to pH 10 with NaOH. The protocolwas derived from the assay described by Englardand Siegel (1969).

called V for a 00-input, W for either01- or 10-input,andX for 11-input. If operationsareto beimplementedthatarenot commutative, a largernumberof signalingsub-stancescouldbeused.It is thenpossibleto encodethesignalline togetherwith thesignal,i.e., thestateof theline.

With thesignalencodingdecidedupon,thepossiblemilieu conditionsat thestartof thereactionareknown.Differencesin thestartingmilieu aremappedby there-action into different absorbancevalues. From the ab-sorbancemeasurementsin Fig. 6 it is possibleto cal-culatehow thereactiongroupstheinputsignalpatterns.Thetimedevelopmentof thegroupingis shown in Fig.7asdistancesamongthe responsesto the3 possiblemi-lieu states. For implementinga desiredinput-outputmap the minimum differencein the responseto sig-nal patternsthat needto be differentiatedis important,sincethis distancecorrespondsto the signal strength.Fig. 8 shows the signal strengthfor the XOR opera-tion. The signalstrengthsfor particularclassificationschangewith theprogressof thereaction.Signalsarriv-ing atdifferenttimeswill thereforemeetdifferentstatesof the reactionmediumand accordinglyaffect the re-actiondifferently. Enzymecontrolleddevicescouldbeusedin this way to integratesignalsin spaceandtime,

500 1000 1500 2000 2500 3000 3500 4000

-0.2

0

0.2

0.4

0.6

0.8

t [s]

∆A

r(c)-r(a)

r(b)-r(a)

r(b)-r(c)

Figure 7: Absorbance difference ( Y[Z ) in response(r) to the three possible milieu states that can resultfrom 2-bit input patterns ( V = 00, W = 01 or 10, X =11). The curves are computed from data in Fig.6, assuming a 1-signal is represented by 66.7 mMMgCl 7 .

in analogyto the spatiotemporalprocessingperformedby naturalbiologicalcells.

t [s]

∆s

500 1000 1500 2000 2500 3000 3500 40000

0.1

0.2

0.3

0.4

0.5

0.6

Figure 8: Time development of XOR signalstrength. The signal strength ( Y]\ ) is given by r(b) -Max( r(a), r(c) ); cf. Fig. 7 for notation. The increasein noise for longer reaction times is associated withthe high absorbance values at those times. Thecurve is calculated assuming the same signal en-coding as in Fig. 7.

Note that the time axesin thefiguresdiscussedhereare relative to the reactionspeed. To implementpat-ternclassificationit is possibleto runthereactionsmuchfaster(aswasdonein theexperimentdiscussedin sec-tion4). However, ahighreactionspeedisnotconvenientfor studyingthetime courseof thereaction.


6 Toward Molecular Co-processors

Our prototypecould be migratedto a more practicaldevice using microfluidics (Hadd et al. 1997; Ungeret al. 2000) and optoelectronics(Zaunerand Conrad1997). Suchlab-on-a-chipmodulescould be adaptedfor desiredfunction by varying the coding of the in-putsand tuning the reactionmilieu (as in the tabletopexperimentsabove), choosingthe reactionparametersusedfor readout(Kessler1994), varying andcombin-ing enzymes,or modifying enzymesthroughdirectedevolution (BeaudryandJoyce 1992;Gaoet al. 1997).Theadditionof moretypesof signalingsubstancesandcoupling to other enzymaticreactionsshouldincreasethe complexity of the patternsthat can be processed.MDH is frequentlyusedasan indicatorreactionin as-saysand thereforeprotocols for linking to other en-zymesareavailable(cf. WilliamsonandCorkey 1969).Ourexpectationis thatthecomputationalcapabilitiesofmany enzymescouldusefullybe investigatedusingthemethodologyoutlinedhere.

The evolutionary adaptationapproachis called fordue to the context sensitive dynamicsof enzymenet-works. This is incompatiblewith conventional pro-grammability. It mightbepossibleto eliminatethecon-text sensitivity, but this would abrogatethe uniquead-vantageof enzyme-basedcomputing(Conrad1988).

We envision migratingelaboratedsignalprocessingmodulesto microchip devices that can be integratedwith conventionalelectronicsignalprocessing.Thede-creasein reactionvolumewould increasespeed.Alter-nativedesignsusingenzymeimmobilizationtechniques(DuVal et al. 1985)andcouplingto diesfor optoelec-tronic readoutcouldbeutilized(Whitaker 1969;Michaletal. 1983).

The tabletopdevice canbe usedto experimentwithsuchhybrid architectures.Servos intendedfor modelairplanescanbeemployedasshown in Fig 9 to operatethevalvesandsyringes.

7 Artificial Neuromolecular Ar chitectures

Automation should speedthe developmentof a use-ful repertoireof biochemicalneurons,but this is still abig task. In the meantimeit is possibleto experiment

Figure 9: Interfacing the artificial enzymatic neuronwith a conventional architecture. Servos from radiocontrolled models can be operated through pulse-width modulation by a digital computer. The servoon the left side steers a T-valve and the servo onthe right positions a syringe pump.

with simulatedneuromoleculararchitectures.The ideais to useneuronsthatdraw on internalsignalintegrationmechanismsto performcomplicatedinput-outputtrans-formsandto combinetheseinto structuresthatcanper-form coherentperception-actiontasks. Our grouphasdevelopeda seriesof suchmodels(e.g.,KampfnerandConrad1983; Kirby and Conrad1986; Conradet al.1989; Ugur andConrad1999). An architecturedevel-opedwith J.-C.Chenis indicative. This consistsof cel-lular automatonneuronsthat modelcytoskeletalsignalprocessing.Thecomplex internaldynamicsof theneu-ronsallows for theevolution of a wide varietyof input-output transforms.Redundantsubnetworks canevolveindependentlyand the resultingneuronsare then har-vestedandcombinedin differentwaysby ahigherlevelevolutionaryalgorithm.Thesystemhasbeenappliedtoa variety of problemdomains,including mazenaviga-tion (ChenandConrad1994),Chinesecharacterclassi-fication (ChenandConrad1997),andmostrecentlytohepatitisdiagnosis(Chen2000).

Architecturessuch as the above provide importanthints aboutthe adaptive proceduresthat would be per-tinent to systemsof real neurons.The simulatedneu-rons of coursehave much less power than would be


possiblewith actualbiochemicalembodiments. Thatusefulfunctionalityis obtainedwith asimulatedsystemsuggeststhat replacingthesimulatedbiochemicalneu-ronswith actualbiochemicalneuronswouldyield muchmorepowerful computationalcapabilities.

8 Dir ections

Theresultsreportedhereappearto haveimplicationsforthe neurondoctrine. Most technicalneuralcomputingmodelsstill assumeessentiallyrathersimple neurons.Many brainmodelstake theircuefrom thesetechnolog-ical systems,despitetheevidentcomplexity of realneu-rons.Thefactthatasingleenzymetypecantransformalinearly inseparableproblemto a linearly separableonestronglysuggeststhat real biological neuronshave ca-pabilitiesthat far exceedthosetypically representedincurrentneurocomputingmodels.

Our working hypothesisis that multi-enzymeex-tensionsof the enzyme-driven systemprototypedherecouldtransformdifficult patterngroupingproblemsintoformsmanageableby conventionaltechniques.Devicesof this typecouldserve asmolecularco-processorsthatprovide novel computationalsynergies for digital ma-chines.In time networksof artificial molecularneuronsmaybeevolvedfor awidevarietyof specialpurposeap-plicationsthatarerefractoryto currentlyavailabletech-nologies. Much remainsto be done,but perhapssomeday it will be possibleto achieve an artificial CleverHans.

AcknowledgmentsThis material is basedupon worksupportedby theU.S.NationalScienceFoundationun-derGrantNos.ECS-9704190,CCR-9610054andEIA-9729818.

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Michael Conrad and Klaus-Peter Zauner- Molecular Computing with Artificial Neurons