Toward Integrated Nanosystems: Fundamental Issues in Design and Modeling

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Copyright © 2006 American Scientific PublishersAll rights reservedPrinted in the United States of America

Journal ofComputational and Theoretical Nanoscience

Vol. 3, 1–10, 2006

Toward Integrated Nanosystems:Fundamental Issues in Design and Modeling

K. Eric DrexlerNanorex, Inc., Bloomfield Hills, MI 48302-7188, USA

Computational design, modeling, and simulation can play a leading role in the development of func-tional nanosystems. Computational methods can describe with useful accuracy a broad range ofcomponents that have not yet been realized; hence they can in many instances be used to guideexperimental in fruitful directions. Further, computational methods can be used to design multiplecomponents that will fit together to make a functional system. This means of coordinating exper-imental efforts can enable the development of components that gain value from their integrationwith other components. Scientific and design-oriented applications of computational methods arefundamentally distinct. Although they frequently describe similar physical systems and use simi-lar methods, science, and design address problems that exhibit an inverse relationship betweenabstract descriptions (theories, designs) and physical systems (specimens, products). This dis-tinction has broad consequences for methodology and for judging the adequacy of computationalmodels. The distinction between the classical protein-folding problem (a scientific challenge) andthe inverse folding problem (a design challenge) provides a concrete illustration. Among functionalnanosystems, those that perform fabrication have a special role because they can enable the pro-duction of other systems. Ribosomes are a widely exploited example. Computational design andsimulation can aid in identifying strategic objectives on paths from current laboratory capabilitiesthrough successive generations of artificial productive nanosystems. This objective highlights thevalue of further developing methods for the design, modeling, and simulation of self-assembly andof self-assembled systems.

Keywords: Nanotechnology, Nanoscience, Nanosystems, Design, Modeling, FabricationDesign.

CONTENTS

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12. The Leading Role of Computational Modeling . . . . . . . . . . . 2

2.1. More Advanced Systems are Sometimes Easier to Model . 23. The Diverse Goals of Computational Modeling . . . . . . . . . . 3

3.1. Science and Design Differ Fundamentally . . . . . . . . . . . 33.2. Protein Design Required the Recognition of a

Design Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.3. System Design Presents Distinct Challenges . . . . . . . . . 5

4. The Strategic Role of Fabrication Technologies . . . . . . . . . . 64.1. Nanofabrication Directs the Motion of Atoms . . . . . . . . 74.2. Self-Assembly Enables Precise Fabrication of Nanosystems 74.3. Productive Nanosystems Offer a Strategic Goal . . . . . . . 84.4. Productive Nanosystems Invite Multi-Stage

Exploratory Design . . . . . . . . . . . . . . . . . . . . . . . . . 85. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1. INTRODUCTION

As technological development moves from scientificinvestigation to system building, the task of designbecomes steadily more important. Successful design of a

technological system requires knowledge that enablesdesigners to describe, with adequate reliability, how thecomponents of the system can be fabricated and assembledand how they will behave and interact. This is as true fordesigning nanosystems as it is for designing the macro-technologies of aircraft, computers, or factories. But howmuch knowledge is necessary for successful design?To ask “how much knowledge?” is, of course,

simplistic—scientific knowledge is not a scalar quantity,but a map of the many-dimensional world of natureand artifacts. Even the notion of “successful design” issimplistic—in every area of technology, some systems aresimple and robust enough to be designed with confidence,while other systems are so complex or so dependent onunknowns that every design becomes a genuine experiment.To advance nanotechnologies from scientific investigationto system building, we must be careful in formulating bothour questions and our standards for judging answers.Nanotechnology researchers apply diverse modeling

methods to diverse physical systems with diverse applica-tions. The modeling methods range from ab initio quantum

J. Comput. Theor. Nanosci. 2006, Vol. 3, No. 1 1546-198X/2006/3/001/010 doi:10.1166/jctn.2006.001 1


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Toward Integrated Nanosystems: Fundamental Issues in Design and Modeling Eric Drexler

chemistry (based directly on fundamental physics),through molecular dynamics (keeping atoms but omittingwave functions), to continuum approximations (omittingboth atoms and wave functions). The physical systemsand their state variables range from crystals with mag-netic degrees of freedom through disordered polymers withmechanical degrees of freedom. Applications are at leastas diverse, ranging from processing molecules using enzy-matic catalysts to processing data using superpositions ofquantum states.This article explores fundamental issues that arise in all

areas of theoretical and computational nanotechnology asquestions advance from the purely scientific to the tech-nological. It pays particular attention to the author’s ownareas of contribution—in protein engineering, molecularmachines, and productive nanosystems—examining theirrelevance to the broader enterprise of nanotechnology andusing them to illustrate universal issues at the junction ofscience, technology, modeling, and design.Section 2 reviews the role of computational modeling

in developing nanotechnologies, showing how computa-tional modeling can, to an unprecedented degree, play aleading role in shaping strategies for research and systemdevelopment. Section 3 examines the diverse goals ofcomputational modeling, showing why effective researchprograms must distinguish among the differing goals ofscience, exploratory design, and design for implementa-tion. Section 4 examines the role of fabrication technolo-gies in the development of nanotechnologies, showing thestrategic role of advances in fabrication and the role ofcomputational modeling in facilitating that advance.

2. THE LEADING ROLE OFCOMPUTATIONAL MODELING

Theoretical and computational methods will play a leadingrole in the development of nanosystems, guiding andspeeding development. Modeling based on these methodscan suggest targets for laboratory development, can reduceexperimental failures by rejecting unworkable ideas, and insome instances can enable reliable prediction and design.Because modeling is not constrained by the current lim-its of our ability to fabricate nanostructures, it can exploreand examine potential targets for development well in

Dr. K. Eric Drexler was born in Alameda, California, in 1955. He studied interdisciplinaryscience, aeronautical and astronautical engineering, and molecular nanotechnology at theMassachusetts Institute of Technology, receiving (respectively) the degrees of S.B. (1977),S.M. (1981), and Ph.D. (1991). An expanded version of his doctoral dissertation has beenpublished as Nanosystems: Molecular Machinery, Manufacturing, and Computation (Wiley-Interscience/1992). He founded the Foresight Institute in 1986 and served as chairman ofthe board through 2002. He is presently the chief technical advisor of Nanorex, Inc. Hiscurrent research focuses on the design and simulation of molecular machines and reactivemolecular tools using molecular mechanics and quantum chemistry.

advance of their physical feasibility. Thus, modeling canhelp to identify fruitful lines of development for researchand investment.Nanofabrication technologies today can produce only a

small subset of the stable, technologically useful structuresthat are physically possible. For example, in the realmof atomically precise covalent structures (other than reg-ular structures, such as crystals), current technologies canproduce little but polymers with controlled sequences ofmonomers and relatively small organic molecules. Preciseconstruction of extended structures with three-dimensionalcovalent bonding is easy to conceive and could readily beaccomplished, but only by using tools that do not yet exist.Developing fabrication technologies that enable the con-struction of a wider range of atomically precise structuresis a fundamental goal for nanotechnology. By simulatingcurrently inaccessible structures and molecular transforma-tions, modeling can explore applications and developmentstrategies for advanced fabrication processes.

2.1. More Advanced Systems Are SometimesEasier to Model

In assessing the adequacy of current modeling capabil-ities for the design of advanced systems and processes,it is important to remember that structures that are lessaccessible to fabrication can be more accessible to mod-eling. For example, the flexible polymeric chains that canbe made today explore, through thermal motion, a set ofconformations that scales exponentially with chain length.The probability of different conformations depends on anoften-delicate balance of energies resulting from Londondispersion forces, electrostatic forces, torsional potentials,and solvent interactions. In some instances (e.g, foldedproteins, DNA junctions) these weak forces cooperate todetermine a single preferred shape for the molecule. Bycontrast, extended structures with three-dimensional cova-lent bonding (e.g., large organic molecules with diamond-lattice frameworks, among many other classes) can formstiff, elastic objects having shapes that are perturbed byweak forces, but not determined by them. The propertiesof these stiff covalent structures increase the simplicity andreliability of modeling and design for several reasons:First, the equilibrium geometry of the structure is typ-

ically the sole minimum of a nearly parabolic potential

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Eric Drexler Toward Integrated Nanosystems: Fundamental Issues in Design and Modeling

energy surface. There is no need to search among differentconformations to compare multiple minima having similarenergies.Second, structural stiffness facilitates free energy calcu-

lations. In flexible polymers, these calculations typicallyrequire estimating integrals of the potential energy overa complex surface in a high-dimensional space, typicallyrequiring evaluation of the energy in many quite differentconfigurations. The free energy of stiff structures, by con-trast, can be estimated accurately knowing only the normalmodes of the structure, which are often available analyti-cally from a single-point calculation.Finally, both geometries and (differential) free energies

are relatively insensitive to errors in the model potential.The difference between the actual physical potential, E(r),and a model potential, E !(r), is equivalent to a perturb-ing force field, !F !(r)= ""#E(r)-E !(r)], applied to themodel. For reasonably accurate models within their rangeof applicability, the perturbing forces !F !(r) are small.In modeling stiff structures, these perturbing forces areassociated with small elastic deformations and correspond-ingly small errors. In flexible polymers, however, the sameforces can be associated with shifts among conformationswith grossly different geometries. Thus, a modeling tech-nique may prove unreliable when applied to soft structuresthat can be made today, yet succeed when applied to stiffstructures that can be made only with more advanced fab-rication systems.Figure 1 illustrates the design of a nanomachine

(a molecular planetary gear) based on stiff covalent struc-tures related to diamond, silicon, and silicon–carbide lat-tices; these structures place it well beyond reach of currentfabrication technologies. The shape and function of itsparts have proved insensitive to differences among severalmolecular mechanics packages.The principle that advances in fabrication can reduce

modeling difficulties has broad application. For example,

Fig. 1. A molecular planetary gear. In mechanical systems, planetarygears convert shaft rotation from high speed and low torque to low speedand high torque. This highly symmetric design is based on stiff covalentstructures that cannot be fabricated today, but can easily be modeled usingstandard molecular mechanics methods. Under operating conditions, theshaft angular speed would be on the order of 109 Hz and the power den-sity (owing to scaling laws that favor small mechanical systems) wouldbe in excess of 109 W/cm3.

the drive for lower defect rates in fabrication reduces theset of physical structures that must be modeled to describeproducts. When products are atomically precise, this setcollapses to a singleton. For another example, the drive tofabricate components with better performance can (whenholding the desired system-level performance constant)provide a margin of safety that makes system performancerelatively insensitive to modeling errors. These observa-tions hold true whether the state variables of functionalinterest are chemical, electrical, magnetic, or quantummechanical.

3. THE DIVERSE GOALS OFCOMPUTATIONAL MODELING

In nanotechnology, as elsewhere, computational modelingaddresses a broad range of questions. These questions dif-fer in surface content—addressing a particular physicalsystem, seeking a particular numerical accuracy—but alsodiffer in their deeper purposes. Distinguishing among thesepurposes is crucial to effective formulation of problems:misunderstood purposes can lead to misdirected questions,misallocation of research effort, and mistaken judgmentsregarding the adequacy of answers. Perhaps the deepestdistinction among purposes for computational modeling isbetween advancing science and analyzing a design. Fur-ther, within the realm of design there is an importantdistinction between refining and validating a particulardesign intended for direct implementation, and exploringa space of design choices in order to describe regionsthat contain particular, workable designs. Because differentpurposes place different demands on theoretical and com-putational studies, it is worth reviewing the implicationsof these familiar distinctions.

3.1. Science and Design Differ Fundamentally

Science and design are closely related, yet in are in somerespects opposites. Although both may deal with the samesorts of physical systems, even describing them using iden-tical physical models, they nonetheless place their modelsin quite different relationships to physical systems (Fig. 2).Scientists take a physical system as given (often after

a lengthy search for a fruitful system to study), then seekto develop a model that describes the system. Designers,by contrast, take a desired functional behavior as given,then seek to specify a physical system that exhibits thatbehavior. Thus, science and design have opposite notionsof dependent and independent variables—one develops amodel to fit the system, the other develops a system to fitthe model. Roughly speaking, science and design addressinverse problems.This difference between science and design corresponds

to different criteria for successful modeling. In science,the inherent goal of precise description establishes theideal of exact equality between physical state variables and

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Fig. 2. Models and physical systems in technology and science. In sci-ence, a physical system has pre-existing properties; measurement yieldsa concrete description; and the concrete description constrains and thusshapes an abstract model (theory) that relates cause to effect. In technol-ogy, an abstract model (system concept) relates desired effects to requiredcauses; design yields a concrete description; and the concrete descrip-tion guides fabrication to produce a physical system with the desiredproperties. Thus, information in science and design flows in oppositedirections. (Of course, practitioners of each generally do both: scientistsdesign experiments, and designers measure their products.)

corresponding model state variables. In design, however,the goal of reliable prediction of function establishes theideal of reliably predicting inequalities between physicalstate variables and design constraints—for example, pre-dicting that an applied force will not exceed the strengthof a component, or that a computation will completebefore the result is needed. Design constraints typicallydefine tolerance bands, and models with substantial butwell-bounded errors often can reliably predict that a statevariable of a physical system will fall within a given toler-ance band. Moreover, designers routinely compensate formodeling errors by choosing designs with correspondinglybroad tolerance bands. Thus, the adequacy of a model asa basis for design can be evaluated only in the context ofa design effort that recognizes and seeks to accommodatethe errors in the model.Science and design also have different criteria for the

basis and generality of models. Science ideally aims todescribe and explain the whole of physical reality assimply as possible. This grand objective drives a searchfor models that apply uniform fundamental principles toall questions. In computational modeling of moleculardynamics, for example, a natural goal is to start fromquantum laws and accurately describe the behavior of anyconfiguration of atoms, from helium gas, to enzymes, tometallic glasses. Limits on algorithms and computationalcapacity, of course, force compromises, resulting a patch-work of methods describing different structures at differentscales of space and time, retreating from ab initio quantummethods to atomistic mechanical models to continuum andlumped-component descriptions.The design perspective differs in treating generality as a

convenience and fundamental physical principles as butone among many sets of useful tools. A designer startswith an objective and seeks to define a physical structurethat will achieve it. Typically, the set of possible struc-tures is highly constrained—consider the limited libraryof micro- and nanoscale structures used to implement

silicon-based digital systems, by contrast to the broadrange of micro- and nanoscale structures in the world as awhole. Moreover, large designed systems are typically par-titioned into components, each described (from the exter-nal, system-level perspective) by a small set of geometricaland operational parameters (e.g., a motor must fit withina particular space, producing torque >x while consumingcurrent <y and producing heat at a rate <z). A designprocess typically requires convenient descriptions of therelationship between structure and behavior for a narrowset of functional components. Whether these descriptionsare based on broad fundamental principles or on narrowempirical generalizations does not affect their utility.Science is judged by the quality of its predictive models,

but predictive models in design are mere tools: providedthe systems in question can be built and then tested toidentify and correct errors, even unreliable predictive mod-els can be tolerated. Indeed, if predictive models wereperfect, testing would be unnecessary. In reality, extensivetesting is the norm in most areas of design practice, andthe basic development sequence—design, model, fabricate,test—often forms a cycle that repeats before a productpasses its acceptance test. The role of modeling is toenable more frequent recognition of design defects atthe modeling stage, hence less frequent rejections afterexpending time and cost for fabrication and testing.These considerations suggest why scientific advances

often have broad utility for design and technology: byimproving the accuracy and generality of the description ofphysical systems, they not only aid the design of familiartechnological systems, but help to open broad new areas totechnological development. Equally, these considerationssuggest why technology so often exploits phenomena thatare reproducible, but poorly understood: limited and defec-tive predictive models are better than none, and (as bio-logical evolution demonstrates) systems can be developedwith no predictive models at all, by sheer trial and error.Organic synthesis provides a good example of a classicengineering capability—constructing specified objects—that has made great progress without strong, quantitativepredictive models. Organic synthesis illustrates anotherpattern, as well: when predictive models are poor, exper-iment plays a guiding role and the pursuit of engineeringgoals merges with scientific investigation.

3.2. Protein Design Required theRecognition of a Design Problem

Protein design is emerging as a useful tool in nanotech-nology. Its intellectual history illustrates the value of dis-tinguishing between problems of science and problems ofdesign.To review, globular protein molecules contain flexible

polypeptide chains that fold to form solid objects ofnanometer scale. Their shapes and surface properties are



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determined by the sequence of amino acids that joined toform them; these amino acids are typically selected fromthe 20 encoded by genes and translated by the molec-ular machinery of ribosomes. The mechanical stiffnessof folded proteins is comparable to that of engineeringpolymers such as nylon and epoxy (but only about 0.01that of a stiff covalent solid). Naturally occurring pro-teins self-assemble to form molecular machines such asenzymes, flagellar motors, and (with RNA) the ribosomeitself. If suitable design techniques can be developed,proteins clearly can serve as a basis for artificial self-assembling molecular machine systems. Further, proteinsshaped to be complementary to non-protein molecularobjects could serve as atomically precise “glue” for self-assembled nanosystems containing other active or struc-tural components.Protein scientists have long pursued solutions to the

“protein-folding problem”: given the monomer sequenceof a natural protein, predict its three-dimensional foldedstructure. Solutions are valuable because sequence infor-mation has been easy to obtain, while determiningfolded structures—and hence the physical basis of proteinfunction—has been difficult.Solving this scientific protein-folding problem was gen-

erally assumed to be a prerequisite for successful proteindesign. On the surface, this dependency seems plausible:solving the scientific problem would enable the predic-tion of protein folds, and protein design aims to produceproteins that fold predictably. Protein-folding researchhas, of course, greatly assisted protein design, yet theassumed dependency was mistaken. As the author arguedin Ref. [1], the problem of designing a sequence thatwill fold to a given structure differs fundamentally fromthe problem of predicting the structure adopted by agiven sequence. To distinguish these two “protein-foldingproblems,” Pabo2 dubbed the design task identified inRef. [1] as the “inverse folding problem;” Ponder andRichards then suggested computational approaches to thisproblem.3 Protein design based on these and further devel-opments has proved successful4 and has now become bothautomated5 and increasingly reliable and routine.6 Resultsinclude proteins that mimic natural folding patterns (butwith different internal and surface structures),6 and designof a novel fold7 (Fig. 3). Moreover, these results haverepeatedly confirmed the initial prediction, based on amargin-of-safety argument, that designed proteins could bemade more stable than natural proteins.1 Progress has alsobeen made on the original, scientific protein-folding prob-lem (in part through insights stemming from the inverse-folding concept,8) yet the computational methods used forthe two problems remain distinct.In protein engineering, distinguishing the design prob-

lem from a related scientific problem was a crucial steptoward success. This distinction will surely prove fruitfulin other areas of nanotechnology.

Fig. 3. A designed protein with a novel backbone structure. Iterativecomputational design yielded TOP7, a 93-residue $/% protein. Producedby the ribosomal machinery of bacteria, TOP7 was found to be foldedand extremely stable. X-ray crystallography revealed a structure with aroot mean square deviation of 0.12 nm from the design model.6 Note thestriking qualitative differences between this protein and the comparablysized structure in Figure 1.

3.3. System Design Presents Distinct Challenges

A goal of nanotechnology is to enable the developmentof nanosystems that integrate diverse nanoscale compo-nents to form complex, functional products. In the worldof macroscopic and microelectronic systems, developmentprojects span wide ranges of time, cost, and complexity.The development of a new computer chip, car, or space-craft can take years, cost millions to billions of dollars, andrequire designs comprising millions of functional compo-nents, each playing a distinct role. System design requiresmethods and levels of abstraction that differ from boththose of scientific investigation and of component-leveldesign. As nanofabrication capabilities advance, broaderareas of nanotechnology will follow nanoscale lithography,advancing into the realm of system design. To understandthe role of theoretical and computational methods in thedevelopment of nanosystems, it becomes important to rec-ognize the distinctive tasks and questions that arise in thedesign of complex systems.Fundamental to system design is the concept of hierar-

chical structure.9 A familiar hierarchy in descriptions ofphysical systems starts with the application of quantumtheory to small structures and short time scales, movingto atomistic and then continuum and lumped-componentmodels to describe larger structures and longer timescales. System design adopts a different hierarchicalperspective—one that focuses on components, sets of com-ponents that form subsystems, which form components at ahigher level, and so on up to level of the total system underdesign (embedded in some environment or broader sys-tem context). This hierarchy can be deep: a wire-designertreats insulation as a component; a motor designer treatsa wire as a component; an aircraft designer treats an elec-tric motor as a component; and a transportation-system



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designer treats an aircraft as a component. As this exampleshows, at the top level of system design, the very conceptof physics-based modeling can lose direct relevance.A system-design process starts at some upper level of

this hierarchy with an overall design concept—a low-resolution sketch of a functional system—then refines thisdesign by adding detail to descriptions of subsystems andtheir relationships, working down to the level of pre-existing components (motors, transistors, atoms). At anylevel, more detailed description and modeling may revealdifficulties or inconsistencies that force revision of thehigher-level design. In a successful design effort, this iter-ative process of moving between higher and lower levelsconverges on a detailed, implementable, and attractivedesign. In early phases of an effort, a designer commonlyworks with a parameterized, high-level description—onein which a multi-dimensional range of systems is describedby a mathematical model in which variables relate (forexample) component volume, power consumption, mass,and so forth. Values for these parameters may be basednot on detailed designs of components, but on estimatesof the properties of well-designed components of therequired kind. Because design works chiefly with inequal-ities and tolerance bands, designers often can compensatefor uncertainty in these estimates by including a marginof conservatism to absorb errors. Where large margins ofconservatism are compatible with adequate system per-formance, early-phase high-level design can proceed withconfidence using quite rough approximations in describingcomponents. This enables preliminary system-level designto proceed in advance of detailed component-level designand modeling. This can enable the formulation of long-term goals.In ambitious, long-term system development projects,

the requirement for novel components may generate sub-stantial research projects. The many technological spin-offs of the 1960s Moon landing program resulted fromthis stimulus to research. Long-term goals in nanotech-nology can likewise motivate a broad research program,including extensive development of theoretical and com-putational methods to support nanosystem design.System-level modeling will be crucial to the design of

integrated nanosystems. Analysis at this level, however,will rely on descriptions of component behavior thatemerge from—but do not exhibit—the physics of interac-tions at the nanoscale. This partial independence of higherlevels from lower levels is a familiar pattern. For example,from an abstract logic-system design perspective, reliablevacuum tubes, CMOS transistors, and molecular electronicswitches are essentially equivalent. From a more concretecomputer-system design perspective, their differences insize, speed, voltage, current, power dissipation, and reli-ability are important, but their differences in molecularstructure and electron quantum states are not.Accordingly, the chief role of theoretical and compu-

tational nanotechnology in the development of integrated

nanosystems will be to support the design and fabricationof nanoscale components and subsystems. Here, the lead-ing role of modeling is clear. In system development, akey to launching a project is confidence that a systemof the intended sort can function—even if many of itsrequired processes and components are not yet demon-strated. Because modeling can precede fabrication capa-bilities (and can model the fabrication process itself),modeling-based research and design can build the con-fidence in success that will motivate the investmentnecessary to achieve ambitious goals.The nature of system development highlights the second

distinction mentioned above, between refining and validat-ing a particular design intended for direct implementation,and exploring a space of design choices in order todescribe regions that contain particular, workable designs.The early phase of system development generates designsthat cannot directly be built—they are preliminary andexploratory in nature, intended to guide not fabrication,but further research leading to more detailed designs. Inthis phase, the purpose is not to specify every detail of thesystem (to enable fabrication), but to define required sub-systems and components, to estimate their feasible capa-bilities, and to determine whether the project is likely toencounter no insurmountable obstacles. In this early phase,the flexibility of parameterized system designs can reducethe pressure on modeling capabilities. If exploratory mod-eling gives results with large error bars, the designercan readily generate an estimate of system performancebased on the corresponding worst-case assumptions. Ifthis worst-case performance is high enough to represent adesirable goal (as will often be the case, given the funda-mental advantages of nanosystems in many spheres), thenconfidence in feasibility can precede precise specificationand complete design.

4. THE STRATEGIC ROLE OFFABRICATION TECHNOLOGIES

Human capabilities in nanotechnology (as in all technolo-gies) are limited by what we can design and by what wecan fabricate. As reviewed above, theoretical and computa-tional methods can make direct contributions to the designof nanosystems, helping to select and validate targets forfabrication. But theoretical and computational methods canalso help in the design of fabrication processes and sys-tems, and hence can make strong indirect contributions tothe fabrication of nanosystems.Among physical technologies, fabrication systems play

a special, strategic role. Other systems can compute, dis-play, transport, and so on, but they cannot make eitherother systems or systems like themselves. Thus, improve-ments in these areas cannot directly, physically advanceother technologies. Fabrication is different because fab-rication systems are responsible for making all oth-ers. Improvements in fabrication can directly, physically



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advance other technologies, and can lay the foundationsfor further advances in fabrication. From this perspective,fabrication forms the trunk of a tree on which all othertechnologies are branches.

4.1. Nanofabrication Directs the Motion of Atoms

Nanofabrication systems include ribosomes, scanningprobe atom-manipulation systems, organic synthesis appa-ratus, and billion-dollar chip-production facilities. Thephysical processes exploited by nanofabrication systemsinclude bond formation in solution, bond formation guidedby molecular machines, molecular self-assembly guidedby intermolecular forces, and lithographically directedetching and thin-film growth. From a modeling per-spective, the fundamental feature common to all theseprocesses is the motion of atoms—an inescapable require-ment for processes that restructure matter. This leads toa focus on molecular dynamics, using quantum methods(or special force fields, such as the Brenner hydrocarbonpotential10) to describe motions that change bonding anda broader class of methods to describe other motions.Most fabrication processes in wide use today operate

on disordered systems. Organic synthesis and molecu-lar self-assembly rely on selective interactions betweenmolecules that collide randomly in solution, yet they canproduce fully ordered molecular and supramolecular prod-ucts. Lithographically directed processes rely on statis-tical processes of etching, deposition, oxidation, and soforth, typically yielding disordered results. Modeling ofthese disordered systems requires the exploration of a largeconfiguration space. In many instances, the products ofthese disorderly physical processes depend on the relativekinetics of competing pathways, or the relative thermody-namic stability of competing end states. In these instances,correctly predicting which pathway or product state willpredominate may require correctly calculating energy dif-ferences in transition states or product states on the orderof kT. The challenge presented by large configurationspaces and sensitivity to small energy differences currentlylimits the use of computational methods in the designingand modeling of (for example) novel organic syntheses.

4.2. Self-Assembly Enables PreciseFabrication of Nanosystems

Many nanofabrication processes yield crystalline struc-tures; it would be useful to be able to design molecularbuilding blocks that assemble to form selected structures.In the general case, crystal structure prediction is difficult.Of the many lattice packing arrangements (crystal poly-morphs) that a molecule might conceivably form, the onethat appears in the actual physical system may dependon very small differences in the free energy of transi-tion states or end states in the crystal growth process.It has recently been stated that “Because we still lack a

general and accurate method for CSP [crystal structureprediction], there is no known example of a designed crys-talline molecular material in wide technological use.”11

This statement, however, exactly parallels the early viewsregarding protein design discussed above: it conflates a sci-entific problem of general prediction with a design prob-lem of specifying structures that behave predictably. Aswith protein engineering, it should be fruitful to distinguishbetween these fundamentally different problems. A focuson design directs attention to computational methods thattake the basic form of a target structure as given (here, alattice) while seeking molecular structures that will favorits formation.Crystal structure design is a special case of atomically

precise molecular self-assembly (as distinct from the self-assembly of micelles or other disordered structures). Strik-ing examples of precise self-assembly (including small2 dimensional crystals) have been produced through thedesign and fabrication of branched, double-stranded DNAstructures (DNA junctions). These structures have beenused to implement simple molecular machines,12 and havebeen proposed as a means for organizing active compo-nents in (for example) molecular electronic systems.13 Thedesign methodology for these structures uses computa-tional methods to identify DNA sequences in which baseswill pair to link particular strand segments while minimiz-ing unwanted pairing between all other segments.In both DNA and protein design, a key requirement for

stable and specific binding is that matching surfaces belarge enough to display multiple molecular features withdistinct properties (of shape, charge, polarity, hydrogenbonding, etc.) These features enable the design of comple-mentary surfaces that exhibit strong cooperative binding,while disrupting binding among other, non-complementarysurfaces. Although scientific studies can benefit from afocus on small, simple structures (which better reveal dif-ferences in elementary binding interactions), design princi-ples favor larger structures (which better conceal errors inestimating elementary binding interactions). Larger struc-tures with larger interfaces enable a designer to controlmore features, offering more opportunities for strength-ening or disrupting selected binding interactions. Largerinterfaces also increase the tolerance for modeling errors:when adding multiple interactions, each expected to bestabilizing, cumulative errors in the total binding energygrow as the square root of area, while the expected bind-ing energy increases linearly. This reduces sensitivity tomodeling errors and enables more reliable design of strongbinding.All these considerations favor larger structures, moti-

vating the use of computational methods to search aspace of design options that tends to grow exponen-tially with structure size. Scientific intuition may suggestthat a larger search space creates a harder problem, butthis perception stems from the scientific goal of gain-ing information, of reducing a set of possibilities toward



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the single, uniquely correct description of a given system.From a design perspective, however, enlarging a searchspace—adding design options—typically creates an eas-ier problem. A larger space of possibilities will generallycontain larger solution-regions (not just a single, correctpoint hidden in a larger space). Adding options offers morepoints of control, more ways to improve a design, andmore paths around obstacles. (This is explored in a protein-engineering context in (Ref. [14]). Here again, the inverserelationship between problems in science and design givesa superficially similar issue—search-space size—a verydifferent significance.Unfortunately, fabricating structures large enough to

self-assemble into well-ordered structures remains a chal-lenge. Instances constructed via general organic synthe-sis have been sporadic and specialized—typically, theyhave been unique structures rather than modular structure-building systems. The flexible and general methods inuse today use large biopolymer molecules, made eitherby organic synthesis (e.g., DNA) or by programmablemolecular machine systems (nucleic acids, made by poly-merases, or proteins, made by ribosomes).

4.3. Productive Nanosystems Offer a Strategic Goal

Fabrication based on programmable biological molecularmachine systems demonstrates striking performance: ribo-somes can build proteins at a rate of #10 monomers persecond with an error rate on the order of 10"4, while poly-merases can build DNA at a rate of #103 monomers persecond with an error rate (via kinetic proofreading) aslow as 10"9 to 10"11 (Ref. [15]). These productive molec-ular machine systems are themselves made of proteinsand nucleic acids and have been induced to self-assemblein vitro. In light of growing capabilities for the designof self-assembling protein and nucleic acid structures, itis natural to consider the design of artificial molecularmachine systems, including productive systems. The ubiq-uitous role of molecular machines in biological sensing,information processing, movement, and molecular trans-formation suggests that artificial molecular machines couldhave broad applications in nanotechnology.A class of molecular machine systems having special

strategic importance to the development of nanotechnol-ogy would be productive systems that, like ribosomes, canfabricate components suitable for building next-generationproductive systems. Productive nanosystems of this classcould open a new range of molecular structures to reliable,programmable fabrication. In the past, the application ofadvances in fabrication to the fabrication of more advancedfabrication systems has sustained a spiral of improve-ment that led from hammered iron to modern nanostruc-tures. Continuing this spiral in the domain of productivenanosystems holds great promise.In considering how machines of this sort might be

designed, we must distinguish the scientific problem of

learning how biological machines work from the problemof designing machines that perform similar tasks. Non-biological approaches may prove simpler. For example,artificial machines could exploit the sequential addition ofreactants to construct monomer sequences (as in a Merri-field synthesis), rather than translating a sequence encodedby an information molecule. Alternatively, a sequence ofmonomers could be bound to a DNA strand in a specificsequence via complementary DNA linkers long enough tobind with high reliability and specificity; a system thatbuilds structures using this monomer-bearing strand wouldresemble a ribosome, but simplified and made more reli-able by the use of larger, pre-bound analogues to tRNAmolecules. The advantage of either class of machine withrespect to ribosomes and DNA polymerases would bean ability to fabricate novel families of molecules; theiradvantage with respect to Merrifield synthesis would begreater speed and reliability, enabling the construction ofmolecules large enough to support reliable self-assembly(of, for example, next-generation machine components).“Artificial ribosomes” are cited in a chemical industryroadmap as a goal for the 3–10 year time frame.16

4.4. Productive Nanosystems Invite Multi-StageExploratory Design

Theoretical and computational methods can help to guidedevelopment because they can describe what has not yetbeen made. Perhaps most significantly, in light of thestrategic role of fabrication technologies, modeling canexplore and guide the development of potential fabricationprocesses and their products. Here, a natural objective is toexplore potential paths for a multi-stage system develop-ment project in which fabrication systems would be usedto produce improved fabrication systems through severalgenerations of technology. As we have seen, in early-stagesystem design, a modest amount of knowledge can sub-stantially reduce uncertainties regarding even quite largeprojects.Preliminary work along these lines17–19 suggests that a

natural, long-term objective for fabrication-system devel-opment is to bridge the implementation gap diagrammedand discussed in Figure 4. This gap separates current fabri-cation technologies, able to make polymeric products (likethe structure illustrated in Fig. 3), from a more capabletechnology able to make products based on stiff covalentstructures (like the gear illustrated in Fig. 1). Theoreticaland computational investigations indicate that these prod-ucts will have large performance advantages relative tocurrent molecular and macroscale machines in areas suchas strength, power density, density and energy cost of com-putation, and breadth of fabrication capabilities.Preliminary, exploratory design suggests that the imple-

mentation gap diagrammed in Figure 4 can be crossedvia a multi-phase, multi-stage development process(diagrammed and discussed in Fig. 5). Current tools and



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Fig. 4. The implementation gap between present and advanced fabrica-tion systems. Productive molecular machine systems today (ribosomes,polymerases) work in solution to make small polymeric structures withrelatively simple functions. Physical considerations and natural directionsfor technological advance suggest the objective of developing produc-tive systems that can make large, complex products from a wider rangeof materials. Performing fabrication in machine-phase systems (in whichmolecular motion results from mechanical conveyance and positioning,rather than from diffusion in a solvent) offers fundamental advantages inthe control of molecular encounters and hence of synthetic reactions.

techniques are not directly able to fabricate systems onthe far side of the gap, but apparently can build next-generation tools that are stepping-stones on paths to that

Fig. 5. Phases vs time in multi-stage development of fabrication sys-tems. Closing the implementation gap (Fig. 4) will require developmentto pass through several intermediate stages, each corresponding to a setof fabrication technologies. The above diagram illustrates the naturalstructure of a multi-stage development process for fabrication systems.Each panel represents the overall state of development at a particulartime. Each region in a panel (reading left to right) represents a specificset of fabrication systems (at some phase in its development), movingfrom those currently available, to next-stage systems, to those furtherfrom implementation. Each arrow represents a fabrication process (atsome phase in its development) that uses the set of systems at its leftto implement the set at its right. The style of a region or arrow repre-sents the phase of development of the corresponding systems or process(see key). Note that some designs are discarded before being imple-mented, and that some are developed well before their physical imple-mentation becomes possible. In the first panel, a continuous chain ofvalid exploratory designs indicates the feasibility of designing and imple-menting one or more corresponding physical systems and processes foreach step. The final panel represents a chain of implemented systems.

ability. Several steps of this sort, followed by scale-upof the resulting high-performance productive nanosystems,apparently can span the implementation gap.In design work, one first considers goals and then means

for implementing them, working backward from objectivesto concrete systems. Here, however, some of the systemscontemplated will require new systems to enable their fab-rication. The purpose of early-phase exploration is not todesign systems that could be built only years from now, butrather to build confidence in the feasibility of the objec-tives, and to better understand how current research effortscan be coordinated to move more directly toward long-term, high-payoff goals.Work to date indicates that achieving these goals would

be of great value to many areas of science and technology.Both biological examples and analyses using standard theo-retical and computational methods indicate that productivemolecular machine systems can enable economical, large-scale fabrication of products (both macro- and nanoscale)built to complex, atomic specifications. The implicationsof this for technology as a whole are profound.Perhaps surprisingly, longer-term objectives can be eas-

ier to model and analyze than are shorter-term objec-tives. One reason is that components constructed from stiffcovalent solids are (as discussed in Section 2.1) easier tomodel than devices constructed from experimentally acces-sible folded polymer structures. Advanced machine sys-tems can be made of these components, and hence inherittheir ease of modeling; designs can then avoid problem-atic conformational degrees of freedom and sensitivity tosmall energy differentials. Further, in advanced systems,the motions of reactive molecules—and hence their oppor-tunities to react—can be strictly controlled. Mechanicaltransport and positioning can prevent unwanted molecularencounters and can sequence and (with careful design ofstiff structures that limit thermal displacements) can pre-cisely direct desired reactive encounters. This degree ofcontrol permits the use of highly reactive species in syn-thesis (where solution-phase with these species would beunspecific), and can make reaction results insensitive tosmall energy differentials among transition and productstates. Overall, these characteristics of advanced designscan reduce sensitivity to modeling errors. A substantial setof components and reactions has been analyzed, but fur-ther work is needed to produce a more detailed picture.Modeling techniques that facilitate the design of reactiontrajectories guided by mechanical constraints would be ofparticular use in this work. The results to date, however,support a system-level analysis that indicates the feasibil-ity of clean, highly productive fabrication systems ableto make a wide range of high-performance macro- andnanoscale products.17

Modeling of productive molecular machine systems canexploit molecular mechanics methods to describe mechan-ical motions (e.g., in molecular transport and positioning),



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together with quantum chemistry methods to describereactive transformations in the synthesis of products. Thisholds true both for early, polymeric systems and forlater systems based on stiff covalent solids, provided thatthese systems are small. Larger systems call for multi-scale modeling techniques in which atomistic descriptionssupport continuum and lumped-component models thatdescribe extended structures and the interaction of subsys-tems. Bridging these levels of description in a consistentmodeling environment suited to system design will be akey challenge.

5. CONCLUSION

As nanotechnology advances, ever more areas of practicewill move from relatively experimental, science-intensivework on simple systems to relatively predictable, design-intensive work on complex systems (a transition alreadyseen in nanoscale lithography for integrated circuits).In this advance, theoretical and computational methodswill speed scientific progress by narrowing the range ofunknowns that require experimental testing, and will speedsystem development by enabling more effective explo-ration and design. By describing systems that have not orcannot yet be made, computational modeling can help toguide progress in nanotechnology by identifying attractivegoals well in advance of their achievement.To fulfill their potential, applications of theoretical and

computational methods must take account of the funda-mental difference between scientific and design problems.Although physical principles are identical in both spheres,the relationship between physical systems and models isessentially reversed. Both the questions and the requiredmethods differ when the problem is to design a system tomeet the requirements of an abstract design model, ratherthan to fit a theoretical, scientific model to a given system.Mistaking a design problem for a scientific problem canobstruct progress (as it did when protein-fold design wasconflated with protein-fold prediction). To design a com-plex, hierarchical system, rather than a simple material ordevice, requires a further shift in perspective. In systemdesign, early development work produces not concrete,directly implementable designs, but abstract, parameter-ized design models that depend on estimates of the perfor-mance of components that have not yet been designed indetail.Because technological advances are paced both by

advances in what can be designed and in what canbe made, a particularly strategic role for computationaland theoretical methods is in the design of systems that

can extend fabrication capabilities. Here, the productivecapabilities of biological molecular machine systems indi-cate a rich set of opportunities. A natural goal is touse biopolymers as building blocks in the constructionof improved polymer-building systems. Turning to longer-term developments, preliminary studies have producedboth detailed designs for stiff, covalent components andexploratory designs of systems that would use and pro-duce such components. These studies indicate that produc-tive nanosystems can eventually achieve the cleanliness,low cost, and productivity of biological molecular machin-ery, while employing different means and producing awider range of products. Owing to the greater stiffnessand reduced configuration space available to stiff, cova-lent components, advanced systems are easier to modelthan those that can be built today. This invites the use ofstandard modeling techniques to explore component andsystem designs well in advance of their implementation.Computational and theoretical methods can both facil-

itate laboratory work today and aid in the identificationof paths to more advanced capabilities. They thus arepositioned to play a central role in advancing and guid-ing developments in many areas within the broad field ofnanotechnology.

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Received: 8 November 2005. Accepted: 9 November 2005.


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