MOLECULAR NANOMACHINES:
Physical Principles
and Implementation Strategies

Eric Drexler


Annual Review of Biophysics and Biomolecular Structure, 23:377-405 (1994)
 

KEY WORDS: nanotechnology, protein engineering, atomic force microscopy, supramolecular chemistry



 
CONTENTS
 
PERSPECTIVES AND OVERVIEW
377
MOLECULAR MACHINES FOR MECHANOSYNTHESIS
379
   Solution Synthesis, Enzymatic Synthesis, and Mechanosynthesis
379
   Principles of Mechanosynthesis
380
   Requirements for Mechanosynthetic Molecular Machinery
382
FABRICATION VIA AFM-BASED MECHANOSYNTHESIS
387
FABRICATION VIA SYNTHESIS AND SELF-ASSEMBLY
387
   Constraints and Strategies for Self-Assembly
388
   Candidate Polymer Systems
389
   Design of Proteins and Protein-Like Molecules
390
   Improving Stability, Predictability, and Solubility
392
   Supramolecular Assembly of Folded Polymers
399
SUMMARY AND CONCLUSIONS
400

 

PERSPECTIVES AND OVERVIEW

In this review, I assess progress in the design and implementation of molecular machine systems by focusing on the fundamental principles of mechanosynthesis and emerging strategies for the synthesis and assembly of large (106 atom) devices. This chapter describes existing knowledge and capabilities from the perspective of molecular systems engineering and examines key objectives in implementing molecular machine systems.

The range of structures termed molecular machines is extraordinarily diverse. Examples include pairs of trypticine moieties with aryl groups that mesh to enforce gearlike corotation (65), polymeric materials that can be driven through cycles of contraction and relaxation by changes in pH (99), zeolite catalysts, enzymes, and the bacterial flagellar motor. A recent review stated that "a molecular machine, commonly an assembly of polymeric molecules, is a structural fabrication that can convert energy from one form or location to another" (99, p. 819). This review instead focuses on a more restricted class of objects–those in which specific molecules combine to form "a structure consisting of a framework and various fixed and moving parts, for doing some kind of work" (35a); the quoted language is a dictionary definition of machine.

Theoretical studies of mechanically guided chemical synthesis (mechanosynthesis) have described some of the useful work that molecular machine systems can perform (18, 24, 61, 67); other studies describe how they can perform computation (20, 22, 24, 63). Thus, besides processing energy, molecular machine systems can also process matter and information. Among these processing functions, mechanosynthesis is of basic importance because it can be used to build molecular machine systems able to perform the other functions. Developing molecular machine systems capable of mechanosynthesis is thus a strategic objective.

In the next section, I compare solution synthesis and enzymatic synthesis with mechanosynthesis and describe the physical principles of mechanosynthetic systems and processes. This description helps define objectives for molecular machine research, indicating the size and nature of the required structures. In the following two sections, I review state-of-the-art in techniques for implementing molecular machine systems and use the requirements of mechanosynthesis to focus attention on key concerns. The first of these sections discusses techniques for molecular positioning using atomic force microscope technologies; a development approach based on these techniques would use mechanosynthesis to build molecular machines. The second reviews progress in protein engineering as a basis for the design and construction of complex functional devices; a development approach based on these techniques would build molecular machine systems via Brownian self-assembly of protein-like molecules to form supramolecular structures. Thus, mechanosynthesis provides a goal for molecular machine development, and AFM positioning and engineering of protein-like molecules provide alternative means toward that end.

MOLECULAR MACHINES FOR MECHANOSYNTHESIS

Suitable molecular machine systems can perform mechanosynthesis, and mechanosynthesis can build molecular machine systems (18, 24). This section first compares mechanosynthesis, enzymatic synthesis, and conventional solution-phase synthesis and then reviews the principles of mechanosynthesis and the implications of these principles for the design of mechanosynthetic devices and for the required capabilities of an underlying molecular machine technology.

Solution Synthesis, Enzymatic Synthesis, and Mechanosynthesis

Currently, chemical synthesis is conducted almost exclusively in solution, where reagent molecules move by diffusion and encounter one another in random positions and orientations. Solution-phase synthesis poses familiar problems of reaction specificity. Although many small-molecule reactions proceed cleanly and have high yields, large molecules with many functional groups present multiple potential reaction sites and, hence, can be converted into multiple products. Single-product yields of 99% are usually considered excellent, yet a sequence of 10,000 steps of this sort would have a net yield of ~10-44, thus reliably yielding zero product molecules from any practicable amount of starting material.

Although a spectrum of intermediate cases can be identified, enzymatic synthesis differs significantly from the standard solution-phase model. Enzymatic reactions (11) begin with reagent binding, which places molecules in well-controlled positions and orientations. The resulting high effective concentrations (often augmented by strain energy, polarization, and catalytic groups) result in high reaction rates. The specificity of the binding interactions determines reaction geometries and results in highly specific reactions. Most alternative reagents will not bind in the active site, and among bound reagents, most alternative reaction geometries are excluded.

Mechanosynthesis as defined here differs from enzymatic catalysis (again, a spectrum of intermediate cases can be identified), yet many of the same principles apply. Anticipated molecular machine systems can position bound reagent molecules with respect to one another and guide the chemical reactions with a degree of specificity not found in solution-phase chemistry (24). The strain energy applied by enzymes is no greater than a fraction of the potential binding energy of the substrate (11), but power-driven mechanosynthetic devices can apply strains of bond-breaking magnitude (24). The provision of enzyme-like reaction environments is also feasible.

One can perform mechanosynthesis by using macroscopic devices, such as scanning tunneling and atomic force microscope (STM and AFM) mechanisms. The first clear example of a mechanically controlled synthesis (albeit of a noncovalent structure) was the arrangement of 35 xenon atoms on a nickel crystal to spell "IBM" (27). STM manipulation of atoms and molecules has been extended, for example, to CO bound to platinum and to silicon atoms on silicon (56). Although these processes still lack the control necessary to build molecular machine systems, they demonstrate the direct, mechanically guided rearrangement of the fundamental building blocks of matter.

Principles of Mechanosynthesis

Mechanosynthetic systems can use several effects to speed desired reactions and to suppress side reactions. Of these, the most basic is control of localized reaction probabilities by mechanical positioning of reactive groups. Solution phase processes provide a convenient point of reference and enable a description in terms of effective concentrations (a more direct description relies on transition-state theory).

EFFECTIVE CONCENTRATION

Consider a reaction between two groups, A and B, that can be attached either to separate molecules free to diffuse in solution or to a single, flexible molecule. The ratio of the intermolecular and intramolecular rate constants defines the effective concentration

(k_intra / s) / (k_inter / Ms) = C_eff (M)

Intramolecular reactions can be accelerated by electronic effects (in which case one might say that the reacting groups have been altered), by release of steric strain (a piezochemical effect), by differential solvation effects, or more commonly, by proximity and orientation. When groups A and B are linked by a flexible polymer, the effective concentrations take on conventional values (less than 55 M, the concentration of water molecules in water). When A and B are held in close proximity and in the correct alignment for a reaction, the effective concentration can be much higher. Thiols in proteins exhibit effective concentrations for disulfide formation of 105 M; in rigid organic molecules, effective concentrations can be 109 M, which is close to a theoretically calculated limit of about 1010 M (11). Where a structure holds two groups apart, the effective concentration can he essentially zero.

COMPLIANCE AND THERMAL MOTION The effective concentration of a favorably positioned and oriented group is greater than or equal to the spatial probability density of a reference point in that group (e.g. a nuclear position) relative to a coordinate system based in the other group. This probability density can be calculated from the temperature and the potential energy surface of the system.

In terms of the compliances c (reciprocal stiffnesses, measured in m/N), the potential energy of a group positioned by a linear mechanical system is

V = 0.5 (Delta x^2 / c_x + Delta y^2 / c_y + Delta z^2 / c_z)

for a suitable choice of coordinates that measure displacement of one group with respect to another, provided that deformation of the groups themselves can be approximated as linear. (Conformational flexibility would violate this condition.)

PROBABILITY DENSITY AND EFFECTIVE CONCENTRATION In both classical and quantum statistical mechanics, the probability density for a harmonic system is the product of the Gaussian probability densities along each of the coordinates. A comparison of classical and quantum mechanical results shows that the classical approximation is adequate for describing most mechanical systems of nanometer or larger scale at room temperature (24); quantum mechanical corrections become substantial (0.1) only at extremes of low temperature, high stiffness, or low mass (e.g. for displacements of individual hydrogen atoms).

In the classical approximation, the Gaussian distribution for a single coordinate is characterized by a standard deviation

At the peak of the Gaussian distribution, the local concentration of a group is

C_local = [ 1000 N_a SQRT(c_x c_y c_z) (2 pi kT)^(3/2) ]^-1 (M),

where Na is Avogadro’s number and energies are in joules. For a system with a compliance of 1 m/N along each of three axes, Clocal approximately equals 400 M at 300 K. If the transverse compliance of the transition state is small compared with the compliance of the positioning mechanism (as is typical), the local concentration calculated

above is approximately equal to the effective concentration (in the absence of orientational effects, which can increase the effective concentration by several orders of magnitude). This formulation neglects the steric interaction of the two reagent groups, which typically increases the effective concentration via excluded volume effects.

A useful model for many mechanosynthetic systems treats the positioning system as applying force along the z axis that presses a group against an unyielding wall. Neglecting stiffness along the z axis, the probability density function is exponential in z, while remaining Gaussian in ×and y. The effective concentration is then

C_local = F [ 1000 N_a SQRT(c_x c_y) (2 pi kT)^2 ]^-1 (M),

where F is the applied force in Newtons. For F = 0.01 nN, with a compliance of 1m/N along each of remaining axes, Clocal = ~150 M at 300 K.

Rate increases from positioning are purely entropic: confining the reacting groups to a smaller volume of configuration space increases the frequency of reactive encounters. Positional control of reagents suppresses reactions at remote sites; along an axis with a compliance of 0.66 m/N, the effective concentration of a group at a distance of –0.3 nm is 108 of the peak (in the absence of reactive groups from other sources). This effect is enthalpic: displacement of the group to a remote reaction site imposes a large strain energy on the supporting structure. Mechanical forces can reduce reaction energy barriers by applying a strain energy that is relieved by passage through the transition state. These favorable enthalpic effects are discussed elsewhere (24).

More accurate models of mechanosynthetic control can be developed from transition-state theory and knowledge of the reaction potential energy surface, but such models are beyond the scope of this review. Models based on effective concentration suffice to show how reaction rates at selected sites can be accelerated, while reactions at alternative, chemically equivalent sites can be suppressed. Provided that the desired reactions occur with high reliability (for a review of requisite conditions, see 24), mechanical control will permit syntheses with 106 sequential reactions to proceed with high yield.

Requirements for Mechanosynthetic Molecular Machinery

A mechanosynthetic device must bind reactive molecules (or groups) and position them relative to an object under construction. The device must be a structure of substantial size and stiffness capable of motion in several controllable degrees of freedom (ideally, six or more). These functional requirements resemble those of an industrial robot arm. Such a device differs substantially from known biological structures and solution-phase systems of small molecules or enzymes.

NEARLY DETERMINISTIC MACHINES

Conventional machines are nearly deterministic, which means they perform a specific series of operations at a predictable rate. Molecular machine systems can likewise be nearly deterministic, provided that the following conditions are met:
  1. Mechanical stiffness is large enough to restrict thermal motion to acceptable bounds.
  2. All energy barriers between acceptable states and error states are large relative to kT.
  3. Input power drives the system through a specific sequence of acceptable states at an acceptable rate.
For a mechanosynthetic system, condition 1 requires that thermal fluctuations seldom bring a positioned group in contact with an inappropriate reaction site, condition 2 requires that the group (and other parts of the structure) not degrade or perform motions analogous to a gear slipping a tooth, and condition 3 requires that the positioning mechanism be driven along a suitable trajectory while binding the right sequence of reactive groups.

Figure 1 Overall geometry of a mechanosynthetic device based on a Stewart platform The lengths of the six Struts are controlled externally, thus enabling the platform to be moved in six degrees of freedom.

A MECHANOSYNTHETIC POSITIONING MECHANISM

Figure 1 illustrates a class of positioning mechanisms based on a Stewart platform. The six struts have controllable lengths and form part of a rigid octahedral framework. Figure 2 illustrates a portion of the range of motion of such a device. The six-strut system gives control of all six degrees of translational and rotational freedom.

Figure 2 A two-dimensional diagram of a portion of the range of motion available to a Stewart platform like that in Figure 1.

DIAMONDOID STRUCTURES

Structures made of diamondoid materials are well suited to molecular machine systems (19, 24, 60). Diamondoid materials are extremely stiff (Young’s modulus typically 250–1000 GPa) and the units of design are individual atoms, which permits great freedom in specifying structures. Investigators have explored useful reactions for synthesizing diamondoid structures by using ab initio molecular orbital methods (67). Figure 3 illustrates a diamondoid bearing (60). Symmetry properties enable properly designed bearings of this class to rotate with energy barriers <0.001 kT (21, 24, 62). Diamondoid structures can serve as a basis for stiff, nearly deterministic systems able to perform mechanosynthetic operations in vacuum at high frequencies (~106 s-1) and with high reliability (error rates < 10-15) (24). Diamondoid systems are a natural long-term goal for molecular mechanical engineering, but their fabrication will require advanced mechanosynthetic capabilities.

Figure 3 A rotary bearing based on a modified diamond structure, designed and analyzed in collaboration with R. Merkle at Xerox Palo Alto Research Center. Interlocking ridges provide a large axial stiffness, while calculated rotational energy barriers are <0.001 at 300 K. Fabrication of such structures will require mechanosynthesis.

POLYMERIC STRUCTURES

Molecular machine systems for mechanosynthesis can be developed in either of two ways: (a) mechanosynthetic capabilities first, which are then used to construct molecular machinery or (b) molecular machinery first, which is then used to perform mechanosynthesis.

Either way, the initial products will be polymeric structures. Mechanosynthetic systems immersed in solution should enable the assembly of complex structures from monomers joined to form an extensively cross-linked polymer. Complex structures made by synthesis and self-assembly will likely be built from polymeric building blocks with fewer cross-links. The feasible Young’s modulus for protein-like structures is presumably no less than that of structural proteins: 4 GPa for wool (containing alpha-helical keratin) (102), 10 GPa for silk (along the beta-strand direction) (102), 10 GPa estimated for bacterial flagella and F-actin (polymers of globular proteins) (73). The feasible modulus of elasticity for cross-linked polymeric structures is presumably in the range of biological and engineering polymers, for example, 1–14 GPa for various resins (97) and 100 GPa for cellulose (102). It may be feasible to stiffen self-assembled structures by incorporating grooves that bind stiffer polymeric chains or chemical precursors to chains or nets.

MECHANOSYNTHETIC POSITIONING WITH POLYMERIC STRUCTURES

The stiffness of a Stewart platform with respect to a surrounding framework structure will be of the same order as the stretching stiffness of one of the struts. A cylinder of modulus 10 GPa with a diameter of 15 nm and a length of 100 nm has a stretching compliance <0.06 m/N. This is a fraction of the tolerable compliance of a reliable mechanosynthetic device, and it provides a margin for additional compliances (e.g. flexibility in reactive groups). Among components of invariant shape, stiffness is proportional to scale, hence structures much smaller than this cylinder may not be adequate.

A more detailed examination of mechanosynthetic devices (24) describes means for binding appropriate reactive molecules and for using externally imposed pressure fluctuations to drive and control operations. The present survey of mechanosynthesis and the requirements it imposes on molecular machine design suffices to identify the fabrication of complex and stiff aperiodic structures as a key development problem.

SELF-REPLICATION

Self-replicating molecular systems have been developed from biological or chemical components. In the polymerase chain reaction, DNA strands replicate in the presence of reagents, enzymes, and cycling environmental conditions (66). RNA molecules can replicate in the presence of activated monomers and a polymerizing enzyme (26). Rebek has designed and synthesized simpler self-replicating molecules that employ DNA-like hydrogen bonding (83). In these systems, molecules serve as templates for the assembly of similar molecules. Both the biological and the chemical systems omit the metabolic complexity of a cell because the experimenter provides the molecular building blocks and other requirements. By employing similar simplifications, mechanosynthetic molecular machine systems driven by externally provided information can be made to build structures like themselves (24, 61).

FABRICATION VIA AFM-BASED MECHANOSYNTHESIS

Atomic force microscope technology (7) enables the placement of tips against surfaces with a positional precision of -0.01 nm and forces as low as 0.01 nN (104). (Thermal drift, however, necessitates frequent corrections in order to maintain a position.) Hansma et al (40) have reviewed the use of AFMs for imaging. These devices have also been used for dissection and imaging of biomolecular structures, such as plasmids (39) and membrane gap junctions (44).

The degree of positional control, together with the relatively low compliance of the tip with respect to transverse displacements (41 m/N), suits AFMs for use as positioning mechanisms in a mechanosynthetic system. The chief remaining requirement is the stiff attachment of molecules (e.g. monoclonal antibody fragments) able to bind and orient reagent molecules from a dilute solution (2325). A system of this sort has not yet been demonstrated, but the physical principles of each component are sufficiently well understood to enable an estimate of the likely properties. Anticipated effective concentrations are on the order of 100 M, which would provide localized reaction-rate accelerations (relative to background reactions) on the order of 108 (24). These accelerations should suffice to build structures containing 105 monomers.

A possible sequence of objectives in pursuing this line of development includes: (a) binding desired molecules to tips in controlled orientations, (b) placing and bonding several reactive groups, and (c) building increasingly complex systems by extending these operations. This approach to molecular machine development has substantial advantages and has been reviewed quite recently (24). The balance of the present review focuses on self-assembling systems, which are more closely related to biological systems and hence to biophysical concerns.

FABRICATION VIA SYNTHESIS AND SELF-ASSEMBLY

Considerable research in organic synthesis focuses on building complex supramolecular structures (3, 46, 53, 55, 83, 105); some of these structures are intended as steps toward molecular machine systems. Biological molecular machine systems form through the self-assembly of folded polymeric structures, chiefly proteins. This section reviews progress in engineering protein-like molecules and its applicability to molecular machine development.

Constraints and Strategies for Self-Assembly

Each step in the self-assembly of a large structure, such as a molecular machine system, involves an encounter between two or more smaller units. All, or all but one, of the units must be soluble; any insoluble unit must be exposed to solvent (units may include solubility aids that are later removed). Each block must bind specifically and with reasonable kinetics; improper binding must be either rare or reversible. Finally, the resulting assembly must be either kinetically stable or stabilized by a further operation.

For stability, covalent bonds usually must join the smallest units: ew other links between small molecules withstand thermal agitation at ordinary temperatures. Polymeric structures have natural advantages for making diverse structures from small units; they are used in biology, and some (peptides and DNA) have well-developed synthetic methodologies. Self-assembled structures must be stiff to serve as good machine components; this requirement favors structures with dense internal packings, ideally of rigid, bulky substructures.

When joining larger units, a combination of many weak interactions typically serves better than the formation of a few strong bonds: weak interactions can combine to give strong binding in a particular geometry but little binding in other geometries. This phenomenon enables reliable assembly steps. Large, asymmetrical structures suitable for use as machine systems could then be assembled using any of several different strategies. One is to give each subunit interface a unique structure with unique binding propensities (as in the ribosome) and mix blocks of all types simultaneously. Another strategy is to emulate solid-phase synthesis by using cyclic exposure to different subunits to control the sequence in which components are added. Structural control then results partly from intrinsic binding specificities and partly from an externally imposed sequence of operations. This approach falls outside recently described, biologically inspired models for controlling self-assembly (55).

The surfaces of assembled components must meet various functional constraints. These will presumably include provision of binding sites for other molecules, such as tools, auxiliary structural elements, and perhaps electronically active components. Binding of other molecules (perhaps followed by their polymerization) can provide a mechanism for altering surface structure after the primary self-assembly process. Binding these molecules may help in meeting the conditions (24) for interfacial sliding with small energy barriers and thereby facilitate the design and fabrication of bearing surfaces.

Candidate Polymer Systems

Self-assembly of polymeric structural units does not demand individual units with stably folded conformations. Nonetheless, building with stable folded units appears advantageous with respect to ease of design, assembly kinetics, and avoidance of unwanted aggregation. Accordingly, the ability to design and synthesize polymers that form stably folded structures is an important objective.

NUCLEIC ACIDS Ease of synthesis and ease of designing matching structures are two reasons for using nucleic acids as building materials. Nonlinear structures can be engineered from DNA; for example, Chen & Seeman have made a framework containing eight DNA junctions, which form a structure with the connectivity of a cube (8). However, the size and geometry of base-paired nucleotides, as well as the presence of a charged backbone, render the design of dense structures awkward. Furthermore, biological systems have (with a few striking exceptions) exploited proteins rather than nucleic acids as a basis for molecular machinery and structural components. Although nucleic acids deserve further consideration, protein-like materials seem more attractive.

STANDARD PROTEINS Naturally occurring molecular machines are built chiefly of standard proteins, which are unbranched polymers of the 20 genetically encoded amino acids. Engineered standard proteins, which can often be made by biological means, can closely resemble natural models, thereby facilitating their design. The chief disadvantages of standard proteins are the limited choices of monomers and chain topology. The de novo design of standard proteins was recently reviewed (89), and successful efforts indicate that engineering of standard proteins could provide a path to complex molecular machine systems. This review, however, focuses on the advantages gained from working with a broader class of structures.

PROTEIN-LIKE MOLECULES A primary motivation for engineering standard proteins is to understand the relationship between structure and stability in natural proteins (95). When engineering nonstandard, protein-like molecules, however, the primary motivation is to take the knowledge gained from engineering standard proteins and use it to make structures that fold more stably and predictably than natural or engineered standard proteins. Potentially useful differences from standard proteins include use of nonstandard amino acids and nonlinear chain topologies, as discussed below.

Researchers can incorporate nonstandard amino acids into proteins by using chemically aminoacylated tRNA in RNA-directed protein synthesis in vitro (4, 9, 72). These techniques have been used to probe protein stability (28, 59), thereby extending and confirming the results of more conventional mutational studies (95).

Scientists continue to review and improve methods for solid-phase peptide synthesis (30, 49); these methods enable wholesale use of nonstandard amino acids. Synthesis of chains that contain over 30 amino acid residues is now routine, although certain sequences are more difficult than others. To the extent that difficult sequences can be predicted (101), experimenters can avoid them by imposing suitable constraints during design (an option not available when making a predetermined natural product). Protein-like molecules (50 residues) can be constructed either directly or by linking several shorter peptides. The latter approach presents serious difficulties if the links must be peptide bonds (e.g. to make a standard protein) but lesser difficulties if links are nonpeptide bonds (e.g. disulfide or metal-ligand bonds) formed between deprotected chains.

OTHER POLYMERS Starburst dendrimers (98) form a diverse class of highly ordered three-dimensional molecular structures. Examples thus far, however, have had high symmetry or flexibility, which precludes their use as building blocks for self-assembled molecular machine systems. Future developments could remove these limitations.

Design of Proteins and Protein-Like Molecules

Natural proteins provide a reference model for the design of a broader class of protein-like molecules. Although the overall thermodynamics of protein stability remain controversial (81, 107), the influence of incremental changes in structure is comparatively well understood (1, 95). Accordingly, differences between standard proteins and proposed protein-like molecules can be used to estimate differences in folding stability. Rose & Wolfenden recently reviewed general issues in protein stability (91).

Yun-yu et al (108) have argued that present methods for computing free energy differences cannot accurately predict the effect of mutations on protein stability because of the difficulty of sampling enough conformations to compute entropic contributions. This prediction limitation, however, need not present difficulties for design. Consider a set of structural changes, each of which is of a type that is statistically favorable but individually uncertain. Because effects on stability are approximately additive, researchers can reliably predict that the joint effect of many such changes will be large and positive.

DESIGN AND STABILITY OF STANDARD PROTEINS DeGrado (13), Mutter & Vuilleumier (70), and Richardson et al (88, 89) have reviewed various aspects of the design of peptides and proteins. Several of the latter have been designed de novo. The first was a4 (14, 15, 86), which has been used as a basis for several subsequent modifications and refinements (37, 38, 82, 85). Others include a 79-residue de novo design (Felix) deliberately modeled on natural protein sequences; this structure folded successfully but with low stability (an estimated 0.8 kcal/ mol) (41). Felix, a four-a-helix design, was as successful on the first try as a b-sheet design (by the same group) was on the ninth attempt; this difference was attributed to the greater modularity of helices and the lesser solubility of b-sheet structures. Another four-helix bundle structure has been designed to present a desired immunogenic determinant (47). A 242-residue a/b-barrel protein has been designed and appears to fold correctly (35). A major conclusion drawn from de novo protein design is the importance of negative design, which seeks not only to stabilize a desired fold but to destabilize alternative folds and patterns of aggregation (14, 88).

Until recently, proteins designed de novo have shown NMR spectra characteristic of disordered cores (89); by modifying an earlier design, Raleigh & DeGrado (82) produced a protein with more native-like characteristics, including a distinct melting transition. These modifications replaced multiple Leu residues (which made up the entire core of a4) with b-branched and aromatic residues and introduced shape complementarity into the packing interactions between helices. A separate effort, which yielded an even more well-ordered core, modified the a4 design by adding two zinc binding sites (38).

NATURAL PROTEINS ARE NEEDLESSLY DESTABILIZED Free energies of protein unfolding are favorable by about 5–20 kcal/mol (17), which corresponds to probabilities of occupying the unfolded state of about 10-4 to 10-15. Because protein folding times are about 10-1 to 103s (11), the mean waiting time to observe an unfolding event in an intact protein with a stability of 15 kcal/mol is over 100 years, which is longer than the lifespan of most organisms.

This waiting time is significant for protein design: because natural selection can only operate on events that occur, evolution has no direct mechanism for favoring proteins much more stable than those observed. The upper end of the stability range observed in vitro could be explained by the presence in vivo of denaturing influences, such as solutes, mechanical stresses, or elevated temperatures, which lead to selection for high stability. Alternatively, stability may sometimes correlate with other evolutionarily favored properties. Finally, free energies of unfolding for highly stable proteins in water are typically extrapolated from data on unfolding in concentrated guanidinium chloride, which may introduce errors.

Because random mutations tend to destabilize any particular folded structure, evolutionary processes (either neutral or adaptive) tend to carry proteins to the threshold of significant instability. Accordingly, the consistently low stability of natural proteins is quite compatible with the goal of constructing artificial proteins of high stability (18). The infeasibility of predicting the folding of natural proteins is also compatible with the goal of designing proteins that fold predictably (18), as has been demonstrated (14).

Improving Stability, Predictability, and Solubility

The design of soluble, stably folded structures can play a central role in the technology of self-assembling molecular machine systems. This section reviews techniques and strategies that appear useful for designing such structures based on existing knowledge of protein stability and the opportunities offered by nonstandard amino acids and chain topologies.

BRANCHED CHAINS Mutter has observed that branched chains have a lower conformational entropy in the unfolded state (because of excluded volume effects) and that branched protein-like structures consistent with a desired fold can be expected to fold more stably and predictably. His laboratory has synthesized several structures (termed template-assembled synthetic proteins) that confirm these predictions (6870).

Applying the same principle with a different synthetic methodology, Hahn et al synthesized a stable 73-residue peptide that had four helical branches (36). They included a substrate-binding site with catalytic residues patterned on chymotrypsin; this peptide cleaved ester substrates at –0.01 the rate of chymotrypsin, with a similar substrate affinity.

LOOPED CHAINS Linking a polymer to form a loop decreases its entropy, and fold-compatible cross-links accordingly favor the folded state by reducing the entropy of unfolding (79). Researchers have developed computer-aided design software for identifying potential loops and disulfide bridges between already-defined structures (74) and used engineered disulfide bonds to stabilize natural proteins (75).

Rizo & Gierasch (90) recently reviewed conformationally constrained peptides containing nonstandard structures. Cross-links between residues i and i+4 can be used to stabilize an a-helix. Formation of amide bonds between side chains during solid-phase synthesis has introduced multiple cross-links in good yields (29).

METAL-ION BINDING Coordination of side-chain ligand groups to a metal ion can result in branched or looped structures of increased stability. Because metal ions can bind selectively to deprotected peptides under mild conditions, they can be incorporated late in an assembly sequence. Metal-ion binding can be quite specific because different groups have affinities for different metals and complexation can be reversible. Furthermore, Cr(II) and Co(II) are labile with respect to ligand exchange, but Cr(III) and Co(III) are relatively inert. Experimenters have introduced the labile forms into metal binding sites in proteins and then oxidized them to the exchange-inert species (100). This process could be useful in self-assembly because it combines the advantages of reversible, cooperative binding with those of a stable product.

Regan (84) recently reviewed the design of metal-binding sites in proteins; among the design efforts reported, the success rate was high. Regan & Clarke modified a4 to incorporate a binding site for Zn(II) with two His and two Cys ligands; the resulting protein bound Zn(II) with an estimated dissociation constant of 2.5 ×10-8 M and was significantly stablized (85). Handel & DeGrado modified a de novo protein design (a4) to incorporate a three-His Zn(II) binding site and observed both binding and substantial stabilization (37). They subsequently incorporated two such sites, which yielded a structure in which the core’s stability was comparable to that of a natural protein (38). In a separate line of development, Pessi et al have engineered a three-His binding site in a protein modeled on a portion of an antibody variable domain (77). Hellinga & Richards designed a metal binding site that appears to bind Hg(II) as they predicted but binds Cu(II) in an unexpected mode (42, 43).

Metal complexes can stabilize isolated helices. One way to achieve such stability is to bind metal ions to pairs of nonstandard, metalligating residues (92); another approach results in an exchange-inert Ru(III) complex that binds pairs of histidine residues (32).

Metal complexes can also link separate peptide chains. For example, researchers have bound various divalent metal ions to assemble triple-helix bundle proteins in which amphipathic peptides are linked to a 2,2'-bipyridene functionality at their N termini (34, 54). A stable Ru(II) complex has been used to make a four-helix bundle protein by linking four pyridyl functionalities, each at the N-terminus of an amphiphilic peptide (33). These structures have branched topologies, the advantages of which were discussed earlier in this review.

MATCHED HYDROGEN-BONDED PAIRS Unlike nucleic acids, standard proteins lack specific pair-wise interactions between monomers (with the exception of cysteine pairing to form disulfides). A study surveying multiple protein structures found no tendency for specific pairs of hydrophobic side chains to associate in protein cores and no tendency for specific pairs to be surrounded by better packed neighbors (6). [In any specific protein, however, the backbone geometry might impose stringent constraints on the allowable set of side chains and conformations (80).]

Nielson et al used standard solid-phase synthesis techniques to prepare polyamides that consisted of thymine-linked aminoethylglycyl units; these polymers bind tightly to DNA with sequence recognition (71). The use of a wider range of hydrogen-bonding groups in this manner would presumably enable the design of protein-like structures containing interfaces that had DNA-like complementarity.

REDUCED BACKBONE FLEXIBILITY Substituting non-Gly for Gly residues or Pro for non-Pro residues decreases the conformational entropy of the unfolded state, thereby stabilizing the folded state (provided that these substitutions are compatible with the folded geometry) (58). Expected improvements are about 1 kcal/mol per residue replaced; observed improvements in natural proteins are smaller but comparable. Helices are stabilized by a-methyl-a-amino acids (dialkylglycines); difficulties in chain synthesis can be overcome by incorporating them as the C-terminal components of protected dipeptides (2).

REDUCED SIDE-CHAIN FLEXIBILITY In several proteins, a buried side chain has multiple conformations discernible in X-ray structures (96), but most buried structures have no conformational freedom. Consequently, burial of flexible structures during folding imposes an entropic cost. The estimated TDS costs for burial of residues in a well-packed core (78) are substantial: Ile, –0.89; Leu, –0.78; Met, –1.61; Phe, –0.58; Val, –0.51 (all in kilocalories per mole at 300 K).

Protein-like molecules can incorporate nonstandard amino acids that have lower conformational entropy per unit volume in the unfolded state. Examples might include amino acids with side chains containing cyclohexyl, norbornyl, or adamantyl moieties. Assuming these ammo acids are incorporated into folded structures that have similar core packing densities, strain energies, and so forth, this reduction in conformational entropy will contribute directly to increasing fold stability. Furthermore, by limiting side-chain flexibility, this strategy should decrease the likelihood of alternative core packings in the folded state and yield a structure of improved predictability and mechanical stability.

INCREASED PACKING DENSITY Richards found that the packing density of protein interiors (the fraction of the volume inside the van der Waals surface) is like that of crystals of small organic molecules. 0.70- 0.78 (87). The local packing densities within a single protein vary from - 0.60 to 0.85; poor side-chain packing correlates with good backbone hydrogen bonding (e.g. in regular secondary structure), while dense side-chain packing correlates with regions of less regular hydrogen bonding (87).

High packing density tends to correlate with stronger van der Waals interactions and burial of more hydrophobic area; hence, provided bad steric contacts are avoided, greater packing density should correlate with greater fold stability and greater mechanical stiffness, which would improve components for molecular machine systems. The variable packing densities in natural proteins suggest that improvements are usually possible. By providing additional side-chain options that add to the set of available shapes, the use of nonstandard amino acids multiplies the number of possible core packings and hence the number of packings with unusually high densities.

Several algorithms identify densely packed sets of side chains and conformations compatible with a specified backbone structure. Some investigators assume that side chains always occupy approximately rotameric states (local minima of strain energy) (16, 80). In other algorithms, simulated annealing is used to search for low-energy packings of a specified set of side chains, including nonrotameric conformations (45, 52).

A rotameric algorithm successfully identified a repacking of a substantial region of the core of a natural protein (42, 43). Another rotameric algorithm that included a molecular mechanics energy, a solvation energy, and an entropic term (also based only on rotameric states) gave good predictions of the relative catalytic efficiency of over 40 related enzyme-substrate combinations and was used to design an altered enzyme that is both highly active and selective for a nonnatural substrate (106). These successes with standard amino acids suggest that the potential of nonstandard amino acids for increasing packing densities can in fact be successfully exploited.

REDUCED TORSIONAL STRAIN A study of high-quality X-ray structures shows that roughly 20% of side chains are nonrotameric (i.e. have at least one torsion deviating by more than 20° from the optimal, rotameric angle); each has a strain energy of more than 1 kcal/mol (94). Even in a protein of only 70 residues, a mean strain energy of 1.5 kcal/mol for 20% of the side chains implies a destabilizing energy of 21 kcal/mol, which is greater than the net stability of the folded state. For a 300-residue protein, the estimated destabilization is 90 kcal/mol.

From a fold-prediction perspective, the prevalence of nonrotameric side chains presents difficulties for rotamer-based algorithms (16, 80). From a fold-design perspective, however, this situation presents some opportunities: if rotamer-based algorithms succeed in designing a dense, hydrophobic core, the resulting structure will be less strained and hence more stable (perhaps by 20 kcal/mol) than an analogous natural protein. Core designs with a relaxed rotameric constraint will have a trade-off between increasing density and decreasing strain. Adding nonstandard side chains to the set of options shifts this trade-off curve in a favorable direction.

REDUCED BAD CONTACTS The mechanical compliances associated with torsional deformations and nonbonded contacts are comparable (though nonlinearities make this a rough comparison). Consequently, one would expect that packing forces, in storing a given amount of energy in torsional strain, would store a comparable amount of energy in bad van der Waals contacts. This effect would more or less double the total strain energy associated with nonrotameric torsions in side chains.

INCREASED CORE HYDROPHOBICITY Dill concludes that hydrophobicity is the chief force driving protein folding and that the pattern of hydrophobicity along a chain chiefly determines the general pattern of its fold (17). Hydrophobicity patterns have been a primary concern in de novo designs. The a4 design has an extraordinarily hydrophobic core and hydrophilic surface and an extremely high stability-- ~ 15.4 kcal/ mol in one version (38). The Felix design does not exaggerate hydrophobicity contrasts and has an unusually low stability -- ~0.8 kcal/mol (41).

Based on a reinterpretation of the calorimetric studies of protein unfolding performed by Privalov & Gill (81) and on electrostatic calculations, Yang et al (107) have concluded that desolvation of peptide units and other polar structures has a large enthalpic cost (~1 kcal/mol per residue) even if these structures are hydrogen bonded in the folded state. This largely cancels the favorable effects of burying and desolvating hydrophobic side chains.

The cost of burying polar structure suggests strategies for increasing fold stability:

1. Increase the bulk of hydrophobic side chains, thereby decreasing the relative amount of polar structure in the interior.
2. Avoid burying polar side chains in the interior. About 7% of the residues in a typical natural protein have polar side chains that are = 95% buried (11). A calculation of the fraction of buried side-chain structure that is polar gives a value of 9.8% (5).
Handel et al argue that buried polar structures provide interactions more specific than hydrophobic contacts and thus play an important role in organizing protein core structures (38). Their use of polar residues to construct metal-binding sites clearly demonstrates this effect, and metal binding can increase folding stability, much as cross-links do. Use of a metal ion–binding strategy is consistent with avoiding most buried polar structures, such as ion pairs and hydrogen-bonded side chains.

Perfluoroalkylated amphiphilic molecules are bulkier and more hydrophobic than their hydrogenated analogues and readily form supramolecular assemblies (51). Fluorinated side chains could also prove useful in engineering protein-like molecules.

NONAQUEOUS SOLVENT SYSTEMS Many water-soluble enzymes remain catalytically active after being lyophilized and dispersed in anhydrous organic solvents such as octane and toluene (50). Furthermore, many are stable to temperatures 100°C and appear to have less conformational flexibility than in water (103). Antibody-hapten binding remains strong and specific in anhydrous organic solvents (93). Because natural proteins (which have evolved under selective pressures favoring marginal stability in aqueous media) can often tolerate anhydrous organic solvents, the design of stable protein-like molecules for anhydrous media is unlikely to prove difficult. The decreased flexibility of proteins in anhydrous media suggests that protein-like molecules may perform better as machine components in the absence of water.

IMPROVED AQUEOUS SOLUBILITY Good water solubility is routinely achieved in engineered helical proteins with a high density of hydrophilic side chains on the surface. Ionic side chains are strongly hydrophilic, and engineered salt bridges can stabilize folded structures. Helix formation, for example, is promoted by the presence of i, i+4 salt bridges between Gly- and Lys+ (57). Extensive use of such side chains also makes folding more predictable by providing a strong contrast in hydrophobicity between surface and interior residues.

SUMMARY Evolution does not maximize the stability of natural proteins. Designs chosen from a larger set of possible structures, with attention focused on maximizing stability, should have substantially greater stability. Table 1 summarizes estimated contributions from the stabilizing mechanisms discussed in this section. The estimated total suggests that application of the strategies reviewed here can increase folding stability by 100 kcal/mol. Even a less thorough and only par tially successful application of these strategies can likely produce structures of excellent stability.
 

Table 1. Feasible stabilization of a nonstandard 70-residue structurea
 
Structural feature
Stability increment (kcal/mol)
Looped chainsb
 16
Metal ion bindingc
 16
Reduced backbone flexibilityd
 14
Reduced side-chain flexibilitye
   7
Increased packing densityf
 14
Reduced torsional strainsg
 21
Reduced bad contactsh
 10
Increased core hydrophobicityi
   5
Sum of estimated increments
103
a All changes are relative to a typical 70-residue natural protein with no disuflied cross-links and assume a design in which all structural features are compatible.
b Based on the change in conformational entropy from forming four 10-residue loops (79).
c Tajen is equal to b.
d Assumes a 1 kcal/mol increment per live residues through use ot dialkylglycines
e Assumes an average improvement of 0.1 kcal/mol per residue through substitution of bulky. inflexible side chains for more flexible side chains in the core.
f Exploitation of nonstandard side chains is assumed to increase packing density by 4% from the mean for proteins (0.74) to a high value for organic crystals (0.78), which is less than dense packings observed in proteins (0.85) (87). The stability increment is estimated from the 1.1 kcal/mol stabilization, which results from filling a cavity the size of a methylene group (48).
g See text; assumes successful core packing with nearly rotameric side chains.
h Estimated at about 0.5 (g).
i Reduction of buried polar groups by 7% through avoidance of buried polar side chains–assuming 1 kcal/mol per polar residue removed.

 

Several of the stabilizing mechanisms discussed here decrease the entropy of the unfolded state: branched chains, looped chains, reduced backbone flexibility, and reduced side-chain flexibility; metal-ion binding is sometimes stable enough to act in this manner. Because these mechanisms operate by reducing the number of possible conformations, they reduce not only the entropy of the unfolded state but the number of potential misfolded states as well. Accordingly, they can be expected to reduce the likelihood that a designed molecule will fold to an approximately correct state but with a disordered core. Stabilization by reduced conformational entropy thus acts to increase folding predictability, thereby acting as an implicit form of negative design (89).

Most of the stabilizing mechanisms discussed here have been demonstrated experimentally, although not all in one molecule. Applied in combination, they seem more than adequate to allow the design of stable protein-like structures of ~70 residues, while leaving extensive freedom in design of the molecular surface, and hence of intermolecular interactions.

Supramolecular Assembly of Folded Polymers

Cram emphasizes the importance of preorganization in self-assembly (10). Folding preorganizes a polymer and places its surface groups in a distinct spatial pattern. Binding interactions between two folded structures can be strong and selective, as illustrated by quarternary structures and protein-antibody binding. Large structures offer more opportunities for complementarity and cooperative binding than do smaller structures: hence the many successes in designing supramolecular assemblies of smaller molecules (10, 53, 55, 105) encourage confidence regarding the design of binding interactions among protein like molecules.

If one models monomers as cubes, then a family of protein-like molecules consisting of 4 ×4 ×4 = 64 monomers would have 16 monomers exposed on each face. If each monomer site permits only five variations in polarity (e.g. nonpolar, hydrogen-bond donor, hydrogen-bond acceptor, positive ion, or negative ion) and only two variations in geometry (bump or hollow), then each monomer site can have one of 5 ×2 = 10 functionally distinct structures, and each face can have one of 1016 different structures. If we use one face structure as a reference, only ~10-4 of a set of randomly generated structures will be complementary in polarity and geometry at more than half of the monomer sites. This calculation suggests that accidental complementarity will be rare, except in regular structures (e.g. the arrays of hydrogen-bonding groups found at the edge of b-sheet).

Most of the previously described strategies for improving fold stability are applicable to designing surfaces for tight, specific binding. The exceptions are altered chain topologies and backbone flexibility, which are irrelevant in already folded structures, and strong hydrophobicity, which would be incompatible with aqueous solubility. Of the others, metal-ion binding can drive quaternary assembly of natural proteins (31), and complementarity of hydrogen bonds and ionic species is common in antibody binding interfaces (12). Dense, low-strain packing of relatively inflexible structures is as favorable in the interface between molecules as in the interior of a single molecule.

Interfaces in quaternary structures are commonly hydrophobic (II), but studies of antibody-protein complexes demonstrate that hydrophilic protein surfaces can bind tightly in water (12). Pellegrini & Doniach successfully used computer simulation of intermolecular interactions to identify the binding sites of three antibodies to hen egg white lysozyme (76), thus suggesting that binding can be modeled well enough to support design.

A sequence of objectives in pursuing the development of molecular machine systems via self-assembly might be as follows:

  1. Develop a more routine ability to design stable, globular, protein-like structures.
  2. Design protein-like structures that assemble to form densely packed regular arrays.
  3. Extend this design capability to assemble complex aperiodic structures of good mechanical stiffness.
  4. Design and build complex structures with sliding interfaces, forming components for molecular machine systems.

SUMMARY AND CONCLUSIONS

The goal of constructing artificial molecular machine systems able to perform mechanosynthesis is beyond the immediate reach of current laboratory techniques. Nonetheless, these systems can already be modeled in substantial detail, and existing techniques enable steps toward their implementation.

Mechanosynthetic systems will rely on mechanical positioning to guide and control the molecular interactions of chemical synthesis. The effective concentration of a mechanically positioned species depends on the temperature and on the stiffness of the positioning system. These concentrations can be large (100 M) and localized on a molecular scale. Background concentrations can approach zero, thus enabling precise molecular control of the locations and sequences of synthetic operations. Researchers have developed concepts for mechanosynthetic systems and defined general technology requirements.

One approach to the fabrication of molecular machine systems is the development of AFM-based mechanosynthetic devices. These would position molecules by binding them to (for example) antibody fragments attached to an AFM tip. Development of suitable monomers, binding sites, and reaction sequences would then be a basis for the fabrication of complex mechanical structures.

Biological molecular machine systems rely on the self-assembly of folded polymers. A review of progress in protein engineering suggests that we have the means to design and synthesize protein-like molecules with well-defined structures and excellent stability. Success in this effort provides a basis for the design of self-assembling systems, and experience with the design and supramolecular assembly of smaller molecules is encouraging regarding the success of this next step.

Development of a molecular machine technology promises a wide range of applications. Biological molecular machines synthesize proteins, read DNA, and sense a wide range of molecular phenomena. Artificial molecular machine systems could presumably be developed to perform analogous tasks, but with more stable structures and different results (e.g. reading DNA sequences into a conventional computer memory, rather than transcribing them into RNA). Self-assembling structures are widely regarded as a key to molecular electronic systems (55, 64), which therefore share an enabling technology with molecular machine systems. Finally, studies suggest that the use of molecular machine systems to perform mechanosynthesis of diverse structures (including additional molecular machine systems) will enable the development and inexpensive production of a broad range of new instruments and products (18, 24, 61). Laboratory research directed toward this goal seems warranted.

ACKNOWLEDGMENTS

I thank W DeGrado, B Imperiali, D Nitecki, C Peterson, F Richards, J Richardson, and K Ulmer for helpful comments on a precursor to this paper, and J Bonaventura, J Bottaro, M Edelstein, B Erickson, T Kaehler, M Krummenacker, R Merkle, and J Ponder for helpful discussions. This work has been supported in part by grants from the Institute for Molecular Manufacturing.


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