Translation of Molecular Order to the Macroscopic Level - Chemical

Review pubs.acs.org/CR

Translation of Molecular Order to the Macroscopic Level Alberto Ciferri* Chemistry Department, Duke University, Durham, North Carolina 27708, United States Author Information Corresponding Author Notes Biography Acknowledgments References

1. INTRODUCTION The gap between the mechanical properties of conventional polymers and those expected for an ordered molecular structure had been commented on in the early 1950s. Polymers such as polyolefins and polyamides were regarded as a mixture of structurally ordered (e.g., crystalline) and disordered (e.g., randomly coiled) domains interwoven with each other as to prevent the development of molecular order throughout a macroscopic sample. The complex shapes, the ordered structures, and the properties of biological materials appeared controlled by properties that the synthetic polymers could never attain. In the 1970s came the important realization that the gap between theoretical and actual properties of polymer could eventually be filled. The report of ultrahigh modulus polyethylene obtained from solid-state deformation revealed the possibility of developing ordered and highly oriented structures even in conventional polymers. The theoretical prediction and the ensuing demonstration of liquid crystallinity in polymers led to the production of highly oriented fibers of polyaramides, which attained mechanical properties close to those of the theoretical crystal. To be sure, defect-free polymeric macroscopic structures, such as those observed with single crystals of low molecular weigh substances, remained an elusive goal. Even liquid crystals exhibited a domain structure with grain size in the micrometer range, and there was no evidence that growth could be tied to mesophase orientation. In the early 1990s two important developments occurred that further and greatly expanded the horizon of polymer science. The main scientific event was the development of supramolecular polymer chemistry. In supramolecular polymerization, the repeating unit is not a simple unit covalently bound to the chain, but it may actually be a polymer or an assembly including compatible and incompatible components. A large number of structures were produced and showed reversible association that depended upon the strength of the supramolecular main bonds. The possibility of reproducing molecular structures organized at the nanolevel and expanded

CONTENTS 1. Introduction 2. Low Molecular Weight Materials and Covalent Polymers 2.1. Single Crystals 2.2. Dendritic Crystals 2.3. Polycrystalline Materials and Semicrystalline Polymers 2.4. Liquid-Crystalline Materials 2.5. Polymer Processing 2.5.1. Processing Crystallizing Polymers from Melt or Solutions 2.5.2. Processing Liquid-Crystalline Melts or Solutions 3. Supramolecular Growth 3.1. Design Strategies 3.1.1. Hard Interactions: Shape Compatibility 3.1.2. Soft Interactions: Distribution 3.1.3. Soft Interactions: Chemical Compatibility 3.2. Growth Mechanisms 3.2.1. Multistage Open Association (MSOA) 3.2.2. Helical Growth (HG) 3.2.3. Growth Due to Phase Changes 3.2.4. Growth over Templates or Formed Structures 3.2.5. Solvent- and Amphiphile-Induced Structurization 3.3. Bond Scrambling and Self-Healing 4. Cellular-Driven Assemblies 4.1. Epithelium 4. 2. Connective Tissue 4.2.1. Collagen II Fibrillogenesis 4.2.2. Collagen Distribution in Connective Tissue 4.2.3. Collagen Distribution in the Vitreous Body 4.3. Nervous Tissue 4.4. Muscle Tissue 5. Engineered Assemblies 6. Concluding Remarks © XXXX American Chemical Society

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Special Issue: Frontiers in Macromolecular and Supramolecular Science Received: March 14, 2015

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but the actual shape may be controlled by growth conditions.1 Defect-free single crystals attain dimensions in the centimeter range and may occur in nature or be artificially produced. Imperfect single crystals, having defects in the positional order (vacancies and dislocations), are known to attain dimensions in the order of meters, as is the case of beryl and gypsum. Diamond is one of the most interesting materials able to form single crystals having unique mechanical and optical properties (Figure 1).2,3

to mesoscopic/macroscopic dimensions appeared closer to the realm of real possibilities. The second development in the 1990s was the emergency of nanotechnology, which aimed at the fabrication of optoelectronic devices characterized by a molecular structure that was highly organized at the nanolevel and restrained to the smallest possible dimensions. Devices based on semiconducting or metallic nanoparticles, molecular switches, nano- and microelectromechanical structures, charge photogenerators, and more were produced. Being restrained to submicrometer dimension, the occurrence of defects was not a main obstacle to the production of devices. The main goal was the production of nanostructured material suitable for specific applications and the nanotools needed for the assemblage of submicrometer devices. Excellent reviews have highlighted chemical strategies for obtaining a variety of supramolecular assemblies and their possible applications not only as mechanical and electronic devices but also in biomedical and biomimetic areas (e.g., signaling of cells and biodynamic structures). Detailed analyses of these functional properties have been presented. However, the vast majority of supramolecular polymers reported in the literature are limited to chain dimensions in the nano to microrange. Several engineered systems (as opposed to selfassembled ones) have also been described. Moreover, most of the work on supramolecular polymers has primarily emphasized chemical approaches for controlling the size, shape, and function of the assemblies. This review critically discusses developments in the science of materials that retain molecular order throughout samples of macroscopic dimensions. In section 2, data for single crystals and conventional covalent polymers are reviewed emphasizing the role of physical parameters such as chain orientation, liquid crystallinity, and defects dissipation. In section 3, supramolecular polymerization mechanisms for linear, helical, tubular, 2D, 3D, liquid-crystalline, dendritic, amphiphilic, and algorithmic model systems are discussed. Some of the strategies used for covalent polymers also apply to supramolecular systems. The emphasis was again on physicochemical approaches such as persistence length, growth coupled to liquid-crystalline orientation, shape recognition, and amphiphilic microsegregation that allow retention of order to the meso- to macrodimensional level. In section 4 the outstanding complexity of biological tissues is considered. The analysis in this section aims to verify if the basic growth mechanisms that coexist with complex biochemical machinery are consistent with those considered in section 3. Extensive discussion of engineered systems is outside the scope of this review. Selected examples of biosynthetic implants in section 5 highlight the complexities of composite structurization. The data and analysis presented highlight the basic science of a new nano to macrotechnology that should eventually encompass and greatly expand the current approach on nanotechnology and produce a variety of materials and functions that mimic the biological systems.

Figure 1. Cubic nanostructure of carbon is translated to a defect-free macroscopic diamond. Reprinted with permission from ref 3. Line Art Drawing of a Diamond by Pearson Scott Foresman, public domain.

The main difficulty in the preparation of synthetic single crystals of diamond is the conversion from the more stable graphitic form of carbon. The costly and extremely slow conversion process is performed either by high pressure-high temperature treatments or by breaking the carbon double bonds using atomic hydrogen above 800 °C. Simpler and extensively used is the production of layers of small nanocrystalline diamond (grains) over a substrate. This material retains some of the characteristics of diamond, but the grain boundaries reduce the periodicity of the structure and affect properties such as the mobility of electrons and photons carriers in microelectromechanical devices.4 2.2. Dendritic Crystals

Dendritic crystals exhibit a branching structure reminiscent of the macroscopic organization of tree-like branches, corrals, and snow flakes5 (Figure 2). For low MW substances, dendritic formation has been attributed to a morphological instability at the end of a growing tip due to poor dissipation of the latent heat of crystallization (generated at the solidification front of a supercooled melt).6,7 If solidification is to proceed, that heat must diffuse away. The instability arises due to the formation of a “bump” at the solidification front. The thermal gradient, steeper near the tip, causes the bump to grow above a critical value. At that point, the propagation of the solidification front is accompanied by a train of side branches growing along the preferred crystallographic direction. Dendritic morphology has received attention for a variety of applications. For instance, Si single crystals and Si multicrystals

2. LOW MOLECULAR WEIGHT MATERIALS AND COVALENT POLYMERS 2.1. Single Crystals

Single crystals are characterized by infinite periodicity (p = ∞) of atomic or molecular crystal spacing along three dimensions. The ideal shape of a crystal should reflect its crystal structure, B

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Figure 3. Fringed micelle model.

tion from a spherulitic to a fibrillar morphology may occur, possibly involving a melting and recrystallization process under stress. Folded chains within lamellae twist, slip, and unfold. Spherulites are transformed into small fibrils parallel to the strain direction. The chains occurring in the less dense interspherulitic regions also become partly aligned.

Figure 2. Snow flakes (ref 5, reproduced from http:// snowflakesbentley.com, not copyrighted).

are important materials as substrates for solar cells. Dendrite size and shape determine the properties of the material.8 The occurrence of multigrains and a distribution of orientation reduce the performance of multicrystal devices. A casting method based on faceted dendrite growth has therefore been used to develop larger grains with a specific orientation. Dendritic patterns are exhibited by a variety of supramolecular9,10 and biological systems.11 The origin of these structures is unrelated to that described above for dendritic crystals. In supramolecular assemblies (Open Assembly in Dendrimers in section 3.2.4), the geometry of the repeating unit, coupled to the interaction at the functional sites, allows growth in successive generations, described by mathematical analysis. Biological dendrites are discussed in section 4.3.

2.4. Liquid-Crystalline Materials

Liquid crystals are formed by low MW materials (such as cholesterol derivatives) and by semirigid polymers having a persistence length larger than ∼50 Å.16 In the case of polymers, it should be appreciated that orientational order rather than positional order (as achieved from crystallization from an isotropic melt) is the most relevant property that allows the translation of molecular order to the macroscopic level. In fact, the main obstacle in ordering a polymer is the geometrical anisotropy of its long chains. The liquid crystal selectively orients the long rigid axes of semirigid macromolecules (section 3.2.3).16−22 Liquid crystallinity is generally a precursor of oriented crystallization.23 A 1982 book highlighted the similarities and differences between the experimental behavior and the theoretical description of low and high MW liquid-crystalline systems.16−19 Anisotropic attractive interactions and repulsive excluded volume effects are, respectively, the prevailing interaction in the two classes of materials. Lyotropic liquid crystals are formed as a result of a phase transition from isotropic solutions above a critical solute volume fraction v* (section 3.2.3). Their structure is characterized by discrete periodicity in one or two dimensions, within domain areas having dimensions in the mesoscopic range. The molecular orientation with respect to the domain axis n is represented by the order parameter S = 1/ 2⟨3 cos2 θ − 1⟩, where θ is the average angle between the molecular long axes and the director (Figure 4a). For a fully ordered system S = 1, whereas for an isotropic system S = 0. Disinclinations (or disclinations), occurring at the boundaries of domains, are defects in the orientation of the directors. There are two basic ways that allow the orientation of the director. The first approach is the application of external conservative fields. The application of an elongational field to unanchored samples will significantly align the directors without greatly altering the order parameter (Figure 4a).21−23The second approach is surface anchoring, for instance, to a thin layer of polyimide spread over a glass substrate and rubbed in a single direction with a cloth. The molecular organization at the nematic−surface interface has been object of extensive investigation.20 There is a thin layer (ξ in Figure 4b) in which anchoring perturbs the nematic structure, possibly attaining a more organized smectic order. The bulk nematic structure, hepitaxially grown, is recovered

2.3. Polycrystalline Materials and Semicrystalline Polymers

Polycrystalline materials of low MW and semicrystalline polymers are characterized by periodicity limited by the size of the constituent grains or “crystallites”. The finite value of periodicity is related to the surrounding defective regions that have no long-range order (p = 0). The ordered regions may be regarded as “domains” having the same structure of single crystals formed because of independent growth of multiple nucleation centers. Their size varies with the conditions under which crystallization occurs and is frequently in the mesoscopic range (ca. 1 μm) but can attain macroscopic dimensions as in the case of galvanized steel.12 Crystallites are usually randomly oriented, producing optical depolarization. For low molecular weight materials, defects may consist of vacancies or dislocations in which the ordered structure is disrupted along a line. Diffusion processes, or suitable thermomechanical treatments, may allow crystallites to join together and exhibit some growth toward larger values of periodicity. For semicrystalline polymers, chain entanglements are trapped within the noncrystalline regions (Figure 3).13 The modification of the crystalline morphology during deformation of polyolefin fibers has been adequately documented.14 Undeformed polyethylene and polypropylene reveal the occurrence of “spherulites” having diameters up to a few millimeters and connected by tie molecules or crystalline bridges. The spherulites are composed of lamellae hosting a folded polymer chain.15 More disorganized conformations prevail for the chains segregated at the boundaries between spherulites. Under one-dimensional elongation, a transformaC

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Figure 4. (a) Order parameter S, domain axis n, and flow-induced domain orientation in liquid crystals. The director is oriented, but the order parameter is unchanged. (b) Schematic representation of director orientation in a nematic liquid crystal anchored to a surface. (Adapted with permission from ref 20. Copyright 1991 IOT.org. Figure 5. (a) Schematic representation of a wet-spinning line. (b) Initial modulus and optical micrographs of PBA as-spun fibers as a function of the pull-off ratio V1/V0 for anisotropic solutions (9 g/dL). Adapted with permission from Alfonso, G. C.; et al. J. Polym. Sci., Polym. Symp. 1978, 65, 213; DOI 10.1002/polc.5070650118. Copyright 1978 Wiley Periodical.

further away from this layer and does retain a uniform director orientation. The competition between an electric field and anchoring is at the basis of the functioning of liquid-crystalline displays. The two ordering approaches should be regarded as a clue to the formation of what might approach single liquid crystals that attain macroscopic dimensions. Upon crystallization at v > v* the highly ordered alignment of the mesophase is normally preserved, allowing self-assembly of an oriented crystalline texture on a macroscopic scale (section 3.2.3).

When compared to the theoretical crystal modulus for polyethylene (250 GPa) these results support the attainment of an extremely high orientation over macroscopic dimensions. Somewhat later, ultrahigh modulus and strength polyethylene (Spectra) were industrially produced using gelspinning techniques. In 2012, Lemstra and co-workers reported a new route to the processing of ultrahigh MW polyethylene. They used plane-strain compression of a molten polymer that had been produced by compaction of a nascent powder.28 They suggested that under these conditions the nascent polymer has a low concentration of chain entanglement, thus greatly favoring the formation of a highly oriented crystalline phase. The assessment of the degree of crystallinity from X-ray data has been often controversial due to inaccuracy in the X-ray crystal density. However, Oth and Flory had earlier investigated the crystallization of highly oriented natural rubber samples.29 They showed that high chain orientation is generally supported by a substantial degree of oriented crystallization. The thermal shrinkage of highly oriented fibers did indeed reflect a firstorder transition between the oriented crystalline and the amorphous phases. The oriented crystallinity does therefore reflect an enhanced transfer of molecular order to the macroscopic level. 2.5.2. Processing Liquid-Crystalline Melts or Solutions. The use of liquid-crystalline solutions of rigid polyaramides for producing ultrahigh modulus fibers began with a 1974 DuPont patent (Kevlar).30,31 Similar properties were also obtained with copolyesters forming thermotropic liquid-crystalline phases.32 Particularly interesting is the formation of oriented, ultrahigh modulus fibers by melt spinning of carbon pitch.33 In the latter case, the mesophase is due to the geometrical anisotropy of large aromatic disklike structures growing during carbonization and evolving toward the hexagonal organization of graphite (Figure 6a). Some semiflexible polymers with persistence length below the critical value for mesophase formation also exhibited high-modulus

2.5. Polymer Processing

The polymer fabrication processes involve methods such as extrusion and spinning (melt, wet, dry, gel, electro). Several methods aim to improve the ordered structure and the mechanical properties of polymers. In spinning, the orientation and final properties of the fibers depend not only upon the flow properties of the polymer and the details of the spinnerette die but also upon the drying steps and the pull-off ratio (extrusion and take up rates V1/V0 see Figure 5a).24−26 Further improvement in molecular order and mechanical properties may be achieved by postspinning thermomechanical treatments. Processing of amorphous polymers generally aims to the production of materials with a definite shape (through interplay of melt viscosity and glass transition) rather than the translation of molecular order to the macroscopic scale. Fabrication processes for a variety of nano- to microtechnological devices are reviewed in ref 26. 2.5.1. Processing Crystallizing Polymers from Melt or Solutions. Crystallites are formed on cooling and become oriented depending upon the extent of deformation during spinning and postspinning treatments. Mechanical properties of conventionally spun nylon fibers are in the order of tensile modulus E ≈ 6 GPa, tensile strength σ ≈ 1 GPa, and extension to break ε ≈ 18%. A pioneering book appearing in 1979 reviewed novel nonconventional approaches for the production of fibers with ultrahigh mechanical properties. Capaccio and Ward’s solid-state deformations (hydrostatic extrusion) of flexible high MW polyolefins (extrusion ratios up to 20) led to the production of polyethylene with modulus up to 170 GPa.27 D

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growth to the orienting effect of phase transitions occurs, and bond scrambling facilitates the disappearance of structural defects. It is therefore necessary to analyze first the design strategies for tailoring supramolecular unimers that associate by virtue of their shape and their hard and soft noncovalent interactions and thereafter their polymerization mechanisms. 3.1. Design Strategies

3.1.1. Hard Interactions: Shape Compatibility. Due to the relatively small intensity of soft noncovalent interactions, the role of shape complementarity acquires particular importance for the stability of supramolecular structures. An analogy has often been suggested between the hard interactions in supramolecular structures and the assembly of building blocks with compatible shape in macroscopic structures. Characteristically, hard interactions occur in structures at either the nano- or the macroscopic level. For instance, the importance of hard interactions is well documented by the formation of ordered liquid-crystalline phases in polymers, which is controlled by excluded volume effects even in the absence of soft interactions (Figure 6a).38 On the other hand, excluded volume effects also control the packing of macroscopic, asymmetric objects. Figure 6b includes typical neighboring coordinations that result from shape recognition. Spheres recognize spheres, and each can coordinate with eight neighbors on a surface, although several voids remain. Hexagons and squares have planar coordination of 6 and 8, respectively, leaving no empty space.39 The hexagonal assembly mode is extensively adopted by structures either at the nano- or at the macroscopic level, e.g., DNA−lipid complexes (cf. Figure 13), muscle fibers (cf. Figure 22), and wasp nests. Figure 6c illustrates how the mixing of elements with different polygonal cell geometry induces curvature, as seen in the supramolecular intracellular membrane, epithelium (section 4.1), and macroscopic football sphere. 3.1.2. Soft Interactions: Distribution. The distribution of soft interaction is characterized by the functionality (F) and the sites (S). F refers to the different directions to which supramolecular bonds are pointing, and S refers to the total number of supramolecular bonds irrespective of their directionality. Examples are given in Figure 7a for unimers having a square shape. Monofunctional unimers (F = 1) only form nongrowing (closed) associations. Bifunctional unimers (F = 2) can form linear (open) polymers or rings and may have several sites (S > 2) pointing along the two directions. Tetrafunctional unimers with F = 4 and S = 4 will form planar assemblies if the bonds point toward azimuthal directions (N, S, E, W) but will form helical structures if bonds point toward E, W, NE, NW (case of actin, section 3.2.2). Since the strength of single supramolecular bonds is usually low, several binding sites S are designed to increase the strength and degree of polymerization (DP) of the assembly (section 3.2.1). The example in Figure 7b illustrates the situation F = 2, S = 8 and the occurrence of sites where branching or termination occurs.38,40 Algorithmic Assemblies. Unimers of similar shapes are usually used in supramolecular polymerization. The example in Figure 7c illustrates a hypothetical assembly of units differing in both shape and distribution of interactions.38 The dynamic assembly−disassembly (scrambling) process of supramolecular bonds should trigger an algorithmic process favoring the selection of partners that optimize both hard and soft

Figure 6. Assembly patterns for particles of different geometrical shape due to purely hard interactions: (a) excluded volume effects for rods and disks, (b) shape coordination and void spaces, and (c) polygonal geometry alteration allows for curvature of the spectrin-rich intracellular membrane. Adapted with permission from Sackman, E. Macromol. Chem. Phys. 1994, 195, 7. Copyright 2009 Wiley-VCH.

properties, which were attributed to a flow-induced formation of a liquid-crystalline phase.33 Figure 5b illustrates the role of the pull-off ratio on the modulus and on the orientation of fibers “as spun” from a liquid-crystalline solution of poly p-benzamide in DMac/LiCl. When the fibers are not under tension (V1/V0 < 1) the modulus is very small, and disordered crystalline morphology is observed. However, just a very small pull-off produces a steep increase of the modulus and, correspondingly, of the orientation. Since it is known that the order parameter is negligibly altered under strain, Figure 5b strongly supports that the increase of the modulus was caused by director orientation.34,35 The most recent variety of poly(p-phenylene teraphthalate), Kevlar 149, is used for ballistic application and advanced composites for aerospace applications. Its modulus attained values in the order of 170 GPa (σ 3.4 GPa and ε 1.7%), comparable to the theoretical limit of 163 GPa. This result represents the most successful translation of molecular order (unperturbed by chain terminals) to the macroscopic level for a synthetic polymer.36 As a conclusion to the present section it appears that investigators of low MW materials and covalent flexible polymers did consistently try to reduce dislocations and entanglements and increase chain orientation to fully develop latent properties. The translation of molecular order to macroscopic polymer dimensions was most successfully achieved for rigid polymers exploiting the orienting effect of liquid-crystalline phases. The latter approach allows removal of residual defects by director orientation or by anchoring. The preservation of molecular orientation in macroscopic samples acquires major significance when more complex supramolecular structures, micelles, and cells are considered in the following sections.

3. SUPRAMOLECULAR GROWTH The translation of molecular order to the macrolevel considered in the preceding section for covalent polymers was based on suitable chemical reactions for the control of DP, on special processing techniques that avoid the formation of defects, and on the orienting effect of phase transitions. In the case of supramolecular polymers, a much larger variety of unimers can self-assemble, extremely large persistence lengths can be attained, and a larger number of polymerization mechanisms often allows the translation of the molecular order to the macroscopic level.37−42 Moreover, coupling of E

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The assembly was designed to reproduce the salient features of the TMV virus illustrated in Figure 8e (section 3.2.4). 3.2. Growth Mechanisms

Following the dictates of supramolecular polymerization, the following mechanisms allow assemblage of linear, helical, and planar structures that in some cases may reach macroscopic dimensions. 3.2.1. Multistage Open Association (MSOA). MSOA, or isodesmic polymerization, occurs when consecutive unimers associate without any cooperative effect. This assembly mode was used in earlier preparations of supramolecular polymers based on single H bonds. The reaction follows the scheme of a typical step-by-step polycondensation without production of water. MSOA has been associated with systems for which in the bulk phase (volume fraction v = 1) the DP follows an approximate square-root dependence upon the association constant38,40−42

Figure 7. Schematic representation of (a) the distribution of functionality and binding sites for model unimers, (b) their polymers, (c) assemblies in which also the shape may vary, and (d) dendrimers. Adapted with permission with a fee from ref 38. Copyright 2005 Taylor & Francis.

DP ≈ K1/2

(1)

The above dependence is illustrated in Figure 9 that also includes the role of the unimer concentration. DPs in the order of 20, obtained by earlier investigators, were consistent with eq 1, taking K in the order of 500 mol−1, independently assessed for the pyridine−benzoic acid association.44 The interest in larger DPs promoted the use of multiple H bonds. From Figure 9, the association constant for three H bonds (5003 ≈ 107 mol−1) should correspond to a DP in the order of 1000 for the ordered AAA−DDD acceptor−donor configuration of the H bonds. These expectations were verified by Meijer and coworkers working with a bifunctional unimer that included various covalent segments terminated by ureidopyrimidone units.45 Dimerization of the latter produced supramolecular chains with four H bonds on each associating surface. The repeating unimer of one specific chain is illustrated in Figure 8b (S = 8, F = 2, see Figure 7b). DPs in the order of 1000 were reported in diluted isotropic solutions, favorably comparing with the dimerization constant of ureidopyrimidone (5 × 107 mol−1 in CDCl3)46 and the AADD−DDAA configuration of the H bonds detectable in Figure 8b.41 Another example is based on the C3-symmetrical discotic molecule illustrated in Figure 8c47,48 with π−π bonds stabilizing a columnar polymer. At variance with the uncoupled reactive ends in the polymer in Figure 8b, a stack of π−π interactions may generate an electronic coupling. Indeed, a C3 polymer having aliphatic side chains formed chiral columnar assemblies upon lowering temperature in isotropic solutions of dodecane. The system had been previously analyzed in terms of the helical cooperative growth mechanism described below.49 However, Meijer and co-workers supported the validity of the MSOA mechanism on the basis of experimental determinations and quantum-chemical calculations.40,41 In particular, they quoted the observation that the stacking energy for face-to-face clusters of unsubstituted benzenes was comparable to that of benzene dimers.50 They also rationalized literature data that showed the role of substituents on the polarization and strength of the simple π−π bond.51 The fully stretched dimensions of the above supramolecular polymers are in the order of micrometers. Covalent DNA is known to attain a length on the order of 1 m.52 Since its persistence length is on the order of 50 nm the molecule is highly folded.53,54 Unfolded single chains attaining macroscopic dimensions appear to require extremely large persistence

interactions. The most stable structure is represented, and the darkened units are rejected due an inappropriate site distribution. The relevance of algorithmic assemblies to the emergency of complex behavior relevant to Systems Chemistry was discussed by Nitschke.43 Dendritic assemblies have special distribution of functionalities and exhibit growth in successive generations. Figure 7d shows the sequential growth of a three-functional unimer (often called “dendron”) according to the divergent method of their synthesis (Open Assembly in Dendrimers in section 3.2.4).39 3.1.3. Soft Interactions: Chemical Compatibility. The various supramolecular associations to be discussed below may be described in terms of an association constant K which is a measure of the total strength of the main-chain bond. In addition to the supramolecular main-chain bond, the individual unimers may often be supramolecular complexes that include internal bonds, often monofunctional ones, which link different parts of the complex. It is this multiplicity of interactions that promotes the astounding variety of supramolecular structures. If two different supramolecular bonds are aligned along the main chain, it is convenient to regard the bond with the lowest strength as the main-chain bond. Main types of supramolecular bonds described in the literature and reviewed in ref 41 are based on localized hydrogen bonds, coulomb interactions, metal-ion coordination, and π−π stacking. Combinations of these localized interactions contribute to the overall stabilization of a given supramolecular assembly. Solvent (e.g., hydrophobic) and amphiphilic interactions may enhance or compete with the above localized interactions. For instance, H bonds are stronger in apolar solvents, coulomb interaction may be modulated by salt or pH changes, and micellar structures are stabilized in a selective solvent. Section 3.2.5 includes a more detailed discussion of solvent and amphiphilic interactions. Figure 8 illustrates several examples in which the stabilization of the unimers and their polymers is based on shape and chemical recognition. The example in Figure 8a reveals a sophisticated strategy to produce a covalent polymer that has side chains with a tapered shape. Stacking interactions of the latter dendrons produce disks that self-assemble into columns. F

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Figure 8. (a) Polymer obtained from ring-opening polymerization of a 7-oxanorbornene substituted with two tapered monodendrons (PD = 23). Assembly into disks of four monodendrons and columns (ref 39). (b) Supramolecular polymer based on bifunctional ureido-pyrimidone units linked to covalent aliphatic segments. The main-chain bond is due to a self-complementary association of four hydrogen bonds in AADD conformation (ref 41). (c) C3-symmetrical acylated 3,3′-diamino 2,2′-bypyridine discotic molecules with apolar side chains R form chiral, helical stacks in alkane solvents at low temperature (ref 40). (d) The discotic amphiphile 2,3,6,7,10,11-hexa(trioxoacetyl)triphenylene forms columnar stacks stabilized by hydrophobic interactions in D2O above a critical volume fraction (ref 60). (e) In the mosaic tobacco virus the guest is a RNA molecule hosted within a cavity of a helical-columnar assembly of 2310 tapered proteins. The induction of helicity in the host (16.3 proteins per turn) is visible (refs 63 and 66). (f) Reversible covalent network based on Diels−Alder chemistry. The unimers include an average of 8.4 ethylene glycol segments that attained a DP ≈ 30 (ref 98). (g) Micelles (dimethylethylamine oxide) form large linear assemblies when the nematic phase appears upon increasing surfactant concentration (ref 59). (h) Supramolecular chains and networks formed by fatty dimers and trimers acids condensed with triamine and linked with urea (ref 97).

is fully compensated by the nucleation of three G-actin unimers. Growth begins as an isodesmic process with the formation of two H bonds per unimer (with a low K) and continues as a cooperative nucleated process (with Kh > K) when any new unimer is stabilized by four H bonds. Van der Schoot49 generalized the thermodynamic approach of Oosawa into a statistical−mechanical treatment that includes a nucleation step. Extended actin filaments have been recently observed in the dendrites that are protruding from the main body of the neural

lengths, in addition to large association constants. In section 4.3 the extremely rigid structure of the neuronal axon will be discussed. The axon attains dimensions in the meter range, and it is based on tubular, rigid supramolecular chains that might have been assembled by MSOA. 3.2.2. Helical Growth (HG). The enhancement of growth due to intramolecular cooperative effects is exemplified by the G−F transformation in actin that was first described by Oosawa in 1959.145,55,56 His model, detailed in Figure 10, shows that the F = 4, S = 4 distribution of the H bonds in the G-actin unimer G

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Figure 9. Theoretical variation of the degree of polymerization with the binding constant (eq 1) according to the MSOA model. Reproduced with permission from ref 41. Copyright 2009 American Chemical Society.

Figure 11. Dynamic assembly of microtubules. (a) Microtubules are produced by the assembly of dark (α) and light (β) tubulin dimers. A slight stagger of the longitudinal protofilaments produces a helical pattern and polarization. GTP to GDP hydrolysis occurs during the polymerization. (b) Time variation of turbidity (right) and birefringence (left) of tubulin solutions (15 mg/mL, pH 6.9) oscillating between isotropic and nematic phases. Measurements at 37 °C followed by quenching at 2 °C. Adapted from ref 61. Copyright American Society of Biochemistry and Molecular Biology. Figure 10. HG scheme for the G → F transformation in actin-ADP. Steady state situation is eventually reached when each end is independently at equilibrium with G unimers. Adapted from ref 55.

rigid covalent polymers (i.e., poly p-benzamide) (section 2.5) and polymers such as DNA that have internally saturated H bonds.1,21 Due to the geometrical anisotropy of the particles, at a critical volume fraction (v*) the excluded volume triggers the formation of a nematic phase according to13

cell (section 4.3).53 Minimum length of the dendrites was in the order of 15 μm. The latter value is close to the reported length of actin filaments (11 μm, DP ≈ 4000) formed in isotropic solution (concentration below 0.04 mg/mL) and to the large values reported for the persistence length (18 μm) of F-actin (phalloidin stabilized + buffer).57 Therefore, the minimum length and the proper rigidity of dendrites are achieved through the HG growth mechanism of actin. The HG mode of assembly was also observed in the formation of fibrin from fibrinogen and microtubules from tubolin (Figure 11a).38 The temperature dependence of the DP for the polymer in Figure 8c was well represented by van der Schoot’s theory, which is however unable to provide evidence for a specific nucleus. The cooperative formation of the helix was tentatively attributed to a conformational transition from a flat to a propeller shape of the arms of each disk, allowing maximization of site interaction.49 Also discussed have been cooperative transitions in which a stable nucleus is not observed and structural cooperativity occurring in covalent systems.41 3.2.3. Growth Due to Phase Changes. Liquid crystallinity and crystallization are cooperative supramolecular processes that inherently lead to macroscopic growth even in the case of low MW substances (section 2.4). In these cases, growth of larger and larger domains occurs at the corresponding critical concentration or temperature. This class of phenomena includes the formation of mesophases by

v* ≈ 3d /q

(2)

For rodlike molecules, v* should be inversely proportional to their axial ratio (length, L/diameter, d). However, in the vast majority of wormlike chains the rigid element that directs the phase transition is the persistence length q (independent upon L).18 It turns out that for PBA and DNA having measured q in the order of 75 and 55 nm, respectively, values of v* larger than the practically accessible range (1−20%) are predicted.38 For more flexible polymers the persistence length is too small to observe the formation of a mesophase even in extremely concentrated solutions.18 Supramolecular Liquid Crystallinity (SLC). At variance with the example described above, growth-coupled-to-orientation is a cooperative effect that enhances growth (up to the persistence length) simultaneously with the formation of a liquid-crystalline phase for supramolecular polymers.13,58−60 This mechanism has not been adequately investigated but is of outmost relevance in the contest of the translation of molecular order to the macroscopic level. In the case of supramolecular polymers, linear growth according to the MSOA or HG mechanism goes on upon increasing unimer concentration. If during such a process a DP corresponding to the persistence length is reached, a mesophase will appear. In such a case the two processes (growth and mesophase formation) are uncoupled H

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but are hierarchically related.58 The process of growth-coupledto-orientation defines instead a peculiar feature of supramolecular liquid crystallinity that has both intra- and intermolecular features and includes chain rigidity in the coupling between growth and alignment.58−60 The theory predicts a critical concentration at which growth will be suddenly enhanced up to the value of the persistence length simultaneously with the formation of the mesophase. It would be extremely difficult to assemble by MSOA or HG a large DP supramolecular polymer that had a weak binding constant. On the other hand, spontaneous growth to large q values would be expected in rather diluted solution according to the SLC mechanism. Considering that the persistence length of tubular systems such as microtubules attains values in the macroscopic range (close to 1 cm),61 it is evident that the SCL mechanism allows for the direct translation of molecular order to macroscopic dimensions. The above considerations suggest a set of practical rules that might be considered when designing supramolecular polymers with tailored chain length and rigidity. The combination of K large and q small allows the attainment of a flexible polymer with large DP. K small and q large allow the attainment of a rigid polymer with a length limited by the value of q. K large and q large allow the attainment of an extremely rigid and long polymer with length possibly exceeding the value of q.58 The theory predicts some stringent conditions (yet to be fully verified) under which the balance of persistence length and association constants triggers an extensive growth. To SLC was attributed the self-assembly of micelle59 (Figure 8g), discotic amphiphiles23 (Figure 8d, see also ref 10), and microtubules60 (Figure 11b). In the latter case, SLC appears to be coupled with helical growth (Figure 11a). Growth Anisotropy. In addition to the enhancement of linear growth promoted by a supramolecular nematic phase, growth may be enhanced by higher order macroscopic mesophases and, eventually, by crystallization.23,62 Hexagonal morphologies have been frequently observed in the solid state, for instance, in the case of keratin and a variety of block copolymers (Figure 12a and 12b).62,63 These structures may often be conceived as a result of a supramolecular polymerization with the axis of longitudinal, nematic order distinct from that representing the lateral supramolecular organization.38,63−65 In the case of

keratin, the longitudinal order corresponds to stacked keratin microfilaments (each composed by eight protofibrils that include strands of α helices64). The less ordered matrix is based instead on a conformationally disordered protein rich in cystine residues that eventually form −S−S− linkages. In general, the lateral chains may interdigitate regularly, randomly entangle, or simply dangle over the lateral surface of the rigid filaments. The hexagonal arrangement in Figure 12c schematizes lateral growth associated with interdigitation in the macroscopic condensed state. Additional examples of lateral (dendritic and hexagonal) growth are described in Open Assembly in Dendrimers in sections 3.2.4 and 3.2.5. Inhibition of lateral growth is described in section 4.2.1. 3.2.4. Growth over Templates or Formed Structures. Short range intermolecular interaction such as host-guest interaction, anchorage to a template or to a complementary molecule, interactions with amphiphilic molecules and membranes promote associations that are often translated to a macroscopic scale. Monofunctional complementary sites produce closed host-guest complexes and monolayers. Multifunctional sites yield polymers, multilayers and dendrimers. In several cases, the template controls both the orientation and the extent (DP) of the association. When this occurs, the patterns of systems with positional order (including occurrence of vacancies) prevail. Closed Host−Guest Complexes and Monolayers. A most interesting example is the interaction between proteins and polynucleic acids occurring in viruses such as TMV (Tobacco Mosaic Virus). As show by Klug,66 the virus includes a helical− columnar assembly of 2310 tapered proteins, 16.3 of them per helical turn, and a cavity in which a RNA molecule is hosted (Figure 8e). The virus can be disassembled in acid solution. Reassembling in the absence of RNA produces a population of dimeric proteins, helical columns, and stacks of flat disks, each disk including 17 capside proteins. When RNA is present, the original 16.3 helical structure is recovered. The underlying assembly process was later described as a supramolecular polymerization of the capside proteins driven by the formation of closed monofunctional bonds with the side chains of the RNA guest.67 The latter acts as a templating crankshaft that organizes the proteins in a helical assembly and controls the length (DP) of the capside. A quantitative theory along the above lines elaborated by van der Schoot and co-workers covered also the formation of related, more symmetrical viruses.68 Planar, monolayers anchored to a surface are exemplified by the S layers that protect the external surface of bacterial cells.69,70 Each S layer protein has an equatorial distribution of H bonds (F = 4, S = 4) and a single south-pole site (F = 1, S = 1) that allows electrostatic binding to the cell surface. In vivo, the cell surface controls the curvature and the size of the S layer, which is preserved during cell division and acts as a “dynamic” membrane. S layers reaching macroscopic dimensions were also grown in vitro over liposomic membranes and solid supports. The occurrence and the elimination of defects in the positional order has also been discussed71 for self-assembled monolayers of alkanethiol on gold. Open Host−Guest Complexes and Multilayers. Sato et al. reported the formation of assemblies based on β-cyclodextrin hosts (having 1−3 binding sites) and two adamantyl guests (having 1−2 binding sites). The formation of polymer-like entities was demonstrated by SLS, DLS, AFM, and TEM

Figure 12. Electron micrographs of cross-sections of (a) block copolymers and (b) Australian fine merino wool. (c) Scheme of the section of a hexagonal, cylindrical assembly of rigid rods with interdigitating side chains. Adapted with permission from refs 67 and 112. Copyright 2005 Taylor & Francis. I

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distribution of the functionalities only allows for the formation of monolayers. However, in the case of dendrimers, the distribution of functionalities is such that each generation may act as a template for the synthesis of the following one. In the absence of a formal theory of supramolecular dendritic polymerization, one may only speculate about the predictive features of the model. An application of the above supramolecular polymerization approach to the dendritic growth of hexagonal DNA−lipid assemblies is discussed in section 3.2.5. It is relevant to note that growth processes have been alternatively described by Tomalia and co-workers in terms of hierarchical structural information transfer, controlled by Critical Nanoscale Design Parameters (CNDPs). Six CNDPs parameters were defined: (1) size, (2) shape, (3) surface chemistry (reactivity), (4) rigidity, (5) architecture, and (6) stoichiometry.83,84 These CNDPs are not inconsistent with the concept of hard (size, shape, architecture, rigidity) and soft (functionality, sites, chemical compatibility) interactions used in this review (sections 3.1.1−3.1.3). The free energy contribution of the individual hard and soft interactions, or of the CNDPs, is lumped up in the supramolecular binding constant, and the DP will be enhanced by cooperative effects. In particular, dendrimer growth occurring within a generational ring is clearly favored over the initiation of a successive ring. Additional cooperative effects, related to liquid crystallinity, will depend upon the shape and flexibility of the assembly, as specified in section 3.2.3. The approach used in this review offers a more detailed description of growth and cooperative effects. On the other hand, the CNDPs have been used to predict nanoperiodic property patterns, leading to the first examples of Mendeleev-type soft matter nanoperiodic tables.85 3.2.5. Solvent- and Amphiphile-Induced Structurization. Assembling by solute−solvent interaction was extensively discussed in refs 38 and 41. The thermodynamic basis for incompatibility was discussed in ref 18. The interaction of a polymer segment with a poor solvent may lead to macroscopic ordering through the formation of liquid-crystalline or crystalline phases. On the other hand, two incompatible segments, supramolecularly or covalently linked, do not phase separate in the absence of a solvent and microsegregate in domains separated by the intersegmental bonds (block copolymers according to the self-consistent mean-field theory65). When a selective solvent is added, the formation of closed micelles, open bilayers, and closed vesicles (liposomes) is observed. On these considerations it is based the widely used strategy of controlling the solubility of supramolecular polymers by the incorporation of suitable side chains. Polar side chains will experience solvophilic interaction, whereas the core of the assembly will experience a solvophobic environment that actually reinforces the cohesion of the structure. In addition to solubility alterations, the actual polymerization mechanism may be altered in particular solvents. For instance, Tobe et al. investigated a macrocyclic structure that polymerized isodesmically in THF but followed a nucleationcontrolled cooperative process in acetone.86 Tikhomirov et al. reported that hydrophobic bases polymerized into rosette nanotubes in hexane and formed Langmuir−Blodgett films at the air−water interface.87 Most interesting supramolecular complexes are formed by the interaction of polyelectrolytes with complementary charged lipids (bilayers or vesicles) and proteins.88−92 DNA−lipid complexes are receiving attention for use in gene therapy. As in the case of the layered polyelectrolytes, the ion-pair interaction

measurements. The structure of polymers is linear when both the host and the guest are bifunctional entities and dendritic when the host and the guest have three and two binding sites, respectively.72 A host−guest supramolecular polymerization based on ABBA-type and cucurbit[8]uril unimers was recently reported. The molecular weight and polydispersity of the supramolecular polymers were controlled by tuning the molar ratio of the host and guest or by tuning the isomer ratio of azobenzene groups in the guest unimers upon irradiation of lights.73 Host−guest interaction has also been exploited for the preparation of supramolecular polymers based on crown ethers and pillar(n)arenes.74 Synthetic host−guest complexes in which no helicity is induced had earlier been described.75 In section 2.4 we reviewed the anchoring of a nematic liquid crystal to a glass surface adequately compatibilized and rubbed. The director orientation of the nematic domains was greatly increased throughout multilayers parallel to the glass surface (Figure 4a). The method favors the translation of molecular order to macroscopic dimensions. Polyelectrolyte multilayers. The assembly process of multilayered anionic and cationic polyelectrolytes is well known.76−80 Since Dekker’s original work76 the area has greatly expanded due to applications in membranes, functionalized surfaces, and more. A 2005 review listed over 1000 references, and current books and reviews are available.77−79 A suitably treated surface is alternatively immersed and washed in the solutions of each of two complementary polyelectrolytes and a final hydrophobic capping layer may be added. Hundreds of complementary layers may be assembled; the thickness of the final film attains macroscopic dimensions and has been reported to increase either linearly or exponentially with the number of layers. Several unclarified issues affect the interpretation of the structure of the PEM. The apparent stability of these “engineered” systems may be due to a frozen state for those systems in which a glass transition sensitive to pH and ionic strength was reported.74 Moreover, the addition of consecutive layers is based on a peculiar assembly mechanism. Since the charged groups are monofunctional ones, a closed supramolecular assembly (Closed Host-Guest Complexes and Monolayers above) of just two oppositely charged polymers would be expected. The current view suggests that under suitable operating conditions each adsorption step results in overcompensation of the charges on the preceding layer, leading to successive charge inversions.79 Open Assembly in Dendrimers. A simple dendrimer, represented in Figure7d, has at its core a trifunctional unit with sites spaced 120°. The first generation attains a functionality of 6, and it is followed by the second generation with a functionality of 12, continuing to double at successive generations. Of more direct concern to the present review is the attainment of meso/macrodimensions. Tomalia and co-workers proposed the strategy of self-assembling shell dendrimers around a dendrimeric core, followed by covalent crosslinking.81 Adopting this approach, van Dongen et al. used generationally homogeneous poly(amidoamine) dendrimers as building blocks for generating homogeneous megamers attaining the size of large protein.82 A simpler approach is to regard dendrimer growth as a form of open supramolecular polymerization over a template. As discussed above in the case of the S-proteins (Closed HostGuest Complexes and Monolayers above), the particular J

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Figure 13. (a) Pictorial representation of the hexagonal complex of short, rigid DNA segments and mixtures of cationic and neutral lipid. Hydrophobic tails interdigitate. Image kindly contributed by Dr. Cecilia Leal using POVRAY (Williamston, Australia). (b) Hexagonal assemblies that grow in successive “generation” are produced with 6, 12, and 18 unimers in successive strata. (c) In the case of a rigid lamellar organization of the cationic lipid (no neutral lipids), DNA segments become sandwiched between bilayers of the lipid. (d) Rupture of a cationic liposome in the presence of a rigid DNA segment results in the formation of a DNA−cationic lipid complex. The latter complex is regarded as a unimer that undergoes supramolecular polymerization by interdigitation with neighboring units. Adapted with permission from ref 90. Copyright 2012 Taylor & Francis.

structure also prevails in systems that include DNA and Gemini surfactants known to form strong bilayers.91 Recent calculations by Perico and Manning place these conclusions on a firm theoretical basis.92 The supramolecular polymerization approach offers a plausible mechanism for the description of complexes between lipids and nucleic acids and also recognizes the fundamental role of the internal cohesion of the interacting assemblies. The above considerations are relevant to some general features of complex biological assemblies. The biological cell discussed in the following sections differs from a lipid vesicle for its ability to envelop and interact with cytoskeleton elements in a relatively large volume (giant synthetic vesicles reaching 100 μm size diameter have been reported but only under nonequilibrium conditions).93,94 Chromatin is based on a sequence of strongly held protein octamers wound up and electrostatically bound to a DNA super helix.95 The spacing between the discotic octamers (15 nm) is smaller than the persistence length of DNA, suggesting that local conformational rearrangements also need to be considered.

is the dominant assembling force. However, the occurrence of hydrophobic interactions directs the formation of hexagonal and lamellar structures such as those evidenced in Figure 13a−c in the case of DNA blended with cationic (i.e., cholesterol derivatives) and neutral (i.e., dioleoylphosphatidyl) lipids. The former lipid is known to form rigid bilayers; the latter is known to favor curved vesicles. The structures in Figure 13a−c were determined by Safinya and co-workers using synchrotron X-ray scattering88 and analyzed theoretically by May and Ben-Shaul by coupling the electrostatic interaction with the elasticity of the lipid layer.89 The formation and growth of these structures was also alternatively described in terms of a dendritic supramolecular polymerization resulting from the superimposition of the electrostatic and hydrophobic components.90 Figure 13d illustrates the supramolecular polymerization approach to the description of the hexagonal structure.90 The scheme assumes that a rigid DNA segment (comparable to the persistence length) destabilizes any preformed liposome to allow ion-pairs formation with single lipid molecules. The resulting uncharged complex is regarded as a unimer that forms a hexagonal array with other unimers through interdigitation of the aliphatic tails of the lipid (see also Open Assembly in Dendrimers in section 3.2.4). Thus, electrostatic interaction stabilizes the unimers, and hydrophobic interaction stabilizes the first and subsequent generations. Inspection of Figure 13b reveals that each unimer is coordinated with six more. The dendritic accretion of successive generations proceeds as 6, 12, 18... The lamellar structure in Figure 13c occurs, instead, when the amount of the curvature-loving lipid decreases. Planar bilayers are formed, disfavoring the curved liposome. DNA is now unable to destabilize the strong bilayer and becomes sandwiched in galleries where a significant number of electrostatic interactions can be established, preserving the structure of the complementary assemblies. The lamellar

3.3. Bond Scrambling and Self-Healing

Healing properties, i.e., the ability of repairing structural damages or defects, are manifested by several covalent, supramolecular, and biological polymers.96−101 Healing mechanisms in biological systems involve complex cellular processes, briefly mentioned in section 4. 2. Healing effects in covalent polymers are often produced through reversible or irreversible alterations of the configuration of switchable bonds, driven by changes of external parameters.99−101 In the case of supramolecular polymers, self-healing effects are produced by reversible junctions based either on supramolecular or on easily reversible covalent bonds. These reversible junctions undergo a “scrambling” process arising from equilibrium dissociation and reassociation with the same or alternative K

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complementary partners.96 The repair mechanism may be regarded as a favorable tool for the translation of molecular order to larger dimensions. The most compelling evidence for self-healing features in supramolecular polymers was the report that macroscopic fracture could be healed when pieces of broken networks were brought into contact. These observations were reported by Liebert and co-workers working with the polymer in Figure 8h that includes a mixture of bifunctional and trifunctional units associated by hydrogen bonds.97 The findings were supported by Lehn and co-workers working with the polymer in Figure 8f that includes reversible covalent polymers based on Diels− Alder chemistry.98 Both polymers attained a DP in the order of 20, adequate to confer Gaussian character to the networks.102 Liebler and co-workers evidenced the roles of deformation rate and temperature and attributed to scrambling the healing of the fracture. Most properties of supramolecular polymers are controlled by the DP (or the equilibrium constant). However, the dynamics of the association−dissociation process are controlled by the rate constants (kd for dissociation).103 Sufficiently large kd and small values of K would ensure an intense bond dissociation even at room temperature. Long-range elasticity is exhibited by the supramolecular networks, notwithstanding the scrambling process. Typical stress−strain (π vs α) curves reported by Liebler and co-workers showed fairly reversible extension up to a 7-fold elongation.97 To shed more light on the elastic behavior of supramolecular networks, the above results were compared with results obtained with covalent networks (particularly the composite ones).99 From the latter studies, we know that in real networks there are selected junctions or weak (strained) cross-links, which are the first ones to rupture under deformation. Dissipation of these weak junctions produces good agreement between experimental data and the theoretical relation between stress, strain, and modulus (M) of the molecular theory of rubber elasticity102−104

π = M(α − α 2)

states.99 The latter conclusion regarding the dissipation of constrains even in the undeformed state of supramolecular networks needs to be confirmed by analysis of the rates of bond association−dissociation, the rates for relaxation of the chain segments trapped between cross-linkages, and the rate of macroscopic deformation. At variance with covalent networks, scrambling may involve a continuous rearrangement of cross-links during extension and recovery cycles, promoting an efficient translation of molecular order during macroscopic elastic deformations.99

4. CELLULAR-DRIVEN ASSEMBLIES In the section above we compared theoretical expectations and experimental behavior for the growth of model synthetic and biological molecules. In the case of isodesmic polymerization, limited size is controlled by the unimer concentration and limiting size is controlled by the equilibrium constant. Cases were also discussed in which the superimposition of cooperative effects (intra- or intermolecular), anchoring to a template, and amphiphilic interactions greatly increase the DP and the positional and orientational order. Cases in which linear growth was distinguishable from dendritic growth along lateral directions were also reviewed. The supramolecular polymers were regarded as living ones due to their open-chain terminals and the dynamic nature of all chain bonds. In addition to the model cases discussed above, a great variety of biological systems are also assembled through supramolecular interactions.105,106 Many perform their functions as soluble materials and may be induced to phase separate in vitro. For instance, the well-known G-quartets, based on four hydrogen-bonded nucleosides hosting a cation in their central cavity, form helical stacks with spacings in the order of 3 Å and hexagonal phases on increasing concentration.105 These observations are consistent with theoretical expectations discussed in section 3.2.3, but there is no evidence that such liquid-crystalline structures occur in vivo or have biological functionality. In the present section we shall be reviewing cases in which structures of macroscopic dimensions and specific functionality are directly assembled in the in vivo systems. Our objective is to verify if the assembly mechanisms theoretically predicted and verified for the model systems in section 3 are indeed operative in the more complex situations of cell-driven materials ordered over a macroscopic scale. The ideal systems to be considered are those represented by the load-bearing and signal-transmitting components of the four basic classes of human biological materials: epithelial, connective, nervous, and muscle tissues (the organs are formed by their various combinations). Biological materials include cells that grow and replicate and biopolymers produced by cells that assemble in the extracellular environment. The identification of supramolecular processes may be relatively simple for the latter systems (cf. collagen, axon). Assemblies of whole cells will also be tentatively considered (cf. hepitelium, muscles). However, cell growth is a complex biochemical process that includes a multiplicity of signals that controls the growth and maintenance of in vivo organisms through the transport of oxygen and nutrients and the elimination of metabolic products. The issue of how nature controls the growth, the limiting size, and the shape of macroscopic tissues and organs has been tackled for over a century by developmental biologists, and it is still a largely unresolved one.107,108 Extensive analyses on what determines cell size were recently presented.109 A review points

(3)

In Figure 14 the stress−strain data for networks of the polymer in Figure 8h are replotted as π/(α−α2) vs 1/α.

Figure 14. Stress−strain isotherm at T > Tg for dynamic networks (data from ref 97) plotted according to the equation of state of the rubber elasticity theory. Reproduced with permission from ref 99. Copyright 2009 Wiley.

Apparent adherence to the elastic equation of state is manifested (the upturn at α ≳ 3 is commonly attributed to the insurgence of nongaussian elasticity).102 Therefore, the data in Figure 14 appear to confirm that scrambling has eliminated the defective strained junctions commonly observed with covalent networks in both the resting and the deformed L

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out that patterns of growth during development are related to control signals originated by genes that produce proteins and morphogens that determine the cell polarity.107 Mechanical forces such as crowding and stretching and other signals from the environment also appear to control cell division and affect the development of an organ. Local stresses acting at the cell surface generate fluid-like behavior that affects morphogenesis and tissue renewal.110 Compensation modes between the number and the dimension of cells have been shown to control the size of plant leaves.111 It is therefore evident that dynamic characteristics affecting cell size and shape, coupled to the controlling signals of a complex biological machinery, do have primary relevance on the morphogenesis of biological materials ordered on a macroscopic scale. However, the general self-assembling principles discussed in the preceding section ought still to be operative. In the present review we highlight the relevance of structural assembly principles to the four macroscopic tissues and avoid reviewing features related to the complex biochemical machinery that assist the formation and maintenance of these tissues in vivo. The latter processes should not represent an insurmountable obstacle to the identification of the underlying self-assembly mechanisms. Selected aspects of this approach could be relevant to the translation of molecular order to the macroscopic level in materials produced in vitro or by exploiting only parts of the complex biological machinery (section 5).

Figure 16. Schematization of the structural organization of (a) stratified ephitelium apical surface, (b) deformation of cell by polarity complex promotes asymmetry, and (c) cylinders or cones anchored to a basement membrane. Adapted with permission from ref 116. Copyright 2008 Nature.

4.1. Epithelium

Epithelial tissue (Figure 15) is characterized by tight connection of constituent cells that may have rough flat,

Polarization is a general cellular feature. Even isotropic cells develop a polarization axis before undergoing cell division. The suggested polarity for tissue morphogenesis in epithelial tissue was attributed to the segregation of cytoplasm and cell− surface protein complexes near the apical surface of the cell. Complexes labeled as Par, Crumbs, and Scrib are known to acquire inhomogeneous distribution within the cell and produce alteration of a regular cylindrical shape (Figure 16b).112 This process is accompanied by the establishment of tight junctions between polarized cells by three different types of transmembrane proteins (i.e., cadherin). These junctions involve supramolecular bonds and are distributed in beltlike regions of adjacent cells just below the apical surface (Figure 16c). The compact, testellized, void-free, and polarized selfassembling network prevents cell migration, conserves the epithelium polarity, represents an effective barrier against pathogens, and protects the whole body (skin) and internal organs. The epithelium also retains fluidity through junction dynamics coordinated with the ongoing cell division process (mitotic spindle orientation) so that the newly formed material may continue to grow within a planar structure.110 Mechanical deformation may induce cell stretching followed by cell remodeling.110,113−117 The alteration of cellular parameters under mechanical stresses is consistent with studies on the elasticity of synthetic phospholipids vesicles and biological membranes.119 Other structural features of the above planar networks are consistent with Figure 6, where design strategies specifically relevant to systems with positional order are schematized. At a given functionality, the void space is influenced by the particular shape. No void space occurs for the assembly of squares with functionality 8 or hexagons with functionality 6. Deviations from the planar structure (allowing bends) are produced by local alteration of the shape of testellized units

Figure 15. Organizations of skin layers. In the epithelium layer (stratified, flat type) cells are close together. In the connective tissue layer fibroblast cells are scattered within a net of extracellular collagen and elastin fibers. (Clemont, Y.; Lalli, M.; Bencsath-Makkal, Z. Light Microscopy Histology Atlas; Creative Common License, Canada. The present author has slightly modified the original for a better fit with text).

cubical, or columnar shape and be arranged in one or more layers. The epithelium does not have vascularization, but cell division and permeation or secretion of selected materials occur through the tissue. The apical (upper) cell surface is exposed to air or fluids, and the basal (lower) cell surface is anchored to the basement membrane. Below the latter, there is the extracellular matrix and the connective tissue where blood vessels are located. Several authors have investigated the basis for the compactness and structural organization of epithelial tissue (Figure 16a).110,112−117 They maintain that the lateral growth of multicellular tissues requires the development of an asymmetry of individual cells (planar cell polarity) and a coordinated alignment of these polarities along the growth direction. M

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and further axial (staggered) growth is possible only through the uncompensated N and C sites at the end of the fibril. The latter are characterized by small association constants that could not justify the formation of the liquid-crystalline mesophase and of the macroscopic fibers which are instead observed.120,121 More complex growth processes must therefore be operative.122 The growth of fibrils was interpreted in terms of the supramolecular liquid crystal mechanism (SLC, Supramolecular Liquid Crystallinity (SLC) in section 3.2.3).122 It was remarked that the initial triple helix does not possess adequate rigidity for the development of conventional liquid crystallinity. In fact, on the basis of its persistence length (11.7 nm), the critical volume fraction would be larger that 0.2 (eq 2), considerably larger than the known solubility limit at neutral pH. However, the persistence length of the growing assembly is expected to be enormously enhanced by the association of more and more triple helices and fibrils.38 Enhanced growth in the longitudinal direction may therefore be associated with the formation of supramolecular liquid crystallinity. The occurrence of particular hierarchical structures (such as collagen helices, fibrils, fascicles, and tendons with diameters of 1.5 nm, 40−500 nm, 5−300 μm, and 100−500 μm, respectively) has also been associated with an improved mechanical performance achieved during evolutionary stages.123,124 4.2.2. Collagen Distribution in Connective Tissue. The random distribution of collagen fibrils that prevails in the connective tissue appears controlled by the way the fibroblasts extrude the precursor procollagen. The fibroblast surface has deep, narrow recesses in which the fibrils and their bundles are assembled. Figure 18 illustrates various fibrils growing

(Figure 16a). Another feature is that the extent of lateral association is expected to be greatly enhanced (with respect to a conventional association of free unimers) by the anchoring of the unimers to the basal membrane. Moreover, deviations from the cylindrical shape (for instance, the quasi-conical shape in Figure 16c) would favor limited bending of the external layer to comply with undulations on the layers underneath. 4. 2. Connective Tissue

In connective tissue, at variance with epithelial tissue, cells are scattered through an extracellular matrix (Figure 15) that includes ground material (dispersed in viscous water solutions) and fibers (rigid collagen, flexible elastin) mostly in a random distribution. Fibers and ground material are produced by cells called fibroblasts. Large variations of fibril diameter and orientation in different tissues have been attributed to different functions, particularly the support of mechanical stress.120 4.2.1. Collagen II Fibrillogenesis. Fibrillar collagen is formed by extracellular self-assembly of triple-helical molecules. A stagger of 67 nm (ca. 1/4 of the molecular length) produces the well-known alternation of high and low electron density in TEM and AFM images.112 Collagen fibrils of type II (found in cartilage) and type I (found in tendons) correspond, respectively, to the association of homotrimeric (α1(II)3) and heterotrimeric (α1(I)2α2I)) triple helices. Fibril length is difficult to measure but attains the macroscopic range (over 10 mm).120 Type II fibrils are thin (diameters up to 40 nm), include several triple helices (1.5 nm diameter), and reveal liquidcrystalline order in the lateral direction. Fibrils of collagen I have thicknesses up to 500 nm and show three-dimensional crystalline order. Extensive lateral growth of type II collagen is inhibited because at some stage of the growth process the external fibril surface becomes decorated by collagen type IX molecules (Figure 17). Crystallization also becomes inhibited,

Figure 18. Fibroblast cells may assume large and complex patterns that allow the growth of collagen bundles (B) with different orientations. N is the nucleus. Small dots are fibrils (Courtesy of Prof. D. E. Birk).

simultaneously within several “bundle-forming” centers (B) on the fibroblast membrane.125 The fibroblasts can crawl around the random matrix, thus producing different orientation of the growing fibrils. Once the collagen matrix is formed it may in turn influence the reptation of fibroblasts.126,127 The directing role of the collagen matrix was evidenced by placing fibroblast cells over oriented collagen gels. The fibroblasts invaded the gels in the direction of orientation.128 Additional evidence for the fibroblast migration comes from extensive work reported by Alberts et al. on the alignment of collagen in scar tissue.126 During wound healing, the regeneration of tissue starts with the formation of the fibrin cloth that stops the bleeding. Within 1 or 2 days the fibroblasts migrate to the area, dissolve the cloth, and begin the synthesis

Figure 17. Schematic representation of staggered growth of collagen II fibrils. The decoration by collagen IX prevents lateral growth. Black dots: N and C terminals of single triple helices. Antiparallel arrangement is depicted, including the possibility of linking fibrils with different orientation. Adapted with permission from ref 134. Copyright 1992 American Society of Biochemistry and Molecular Biology. N

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of a new collagen matrix. In adult humans, the remodeled tissue exhibits larger collagen density, larger fiber diameters, and differences in the orientation with respect to the original tissue. Remarkably, no such differences were reported for fetal tissue. There is indeed an evolution of the morphology and properties of connective tissue with age. An increased rigidity of tendons with age has long been known. A tendency of collagen to crystallize or become cross-linked was earlier suggested.130 Some of the alterations appear to be controlled by biochemical events through a connective tissue growth factor (CTGF) protein.129 However, the decay of connective tissue could also be driven by structural properties. In particular, a thermodynamic segregation of the components would be expected from the incompatibility of rigid molecules with a disorganized matrix.131 A possible desegregation was considered for synthetic composite materials when its occurrence is prevented by the rigidity of the glassy matrix.131 4.2.3. Collagen Distribution in the Vitreous Body. More elaborated is the radial organization of collagen fibrils within the vitreous gel of the human eye (Figure 19).132−135

Figure 20. (a) Proteoglucan includes a core protein (CP, i.e., collagen IX) with side chains bound to chondroetin sulfate (CS) and to a multifunctional globular protein bound at the N terminal (G1) and able to establish supramolecular bonds between the proteoglycan and hyaluronic acid (HA). (b) Network structure of the vitreous body shows collagen II fibrils (Coll.fib.) chemically bound to proteoglycans in an antiparallel manner. The latter complexes are bound to a hyaluronan chain at the G1 site of the proteoglycan. Additional, unbound HA swells the network: open circles, water; minus sign, fixed negative charges. Reproduced with permission from ref 135. Copyright 2007 Taylor and Francis.

in the vitreous cortex are anchored and aligned along the retinal surface. Moreover, the upper left-hand side suggests the occurrence of a splay-type deformation that is reminiscent of that occurring with anchored and planarly oriented liquid crystals under an electric field.136 The splay mechanism might indeed be responsible for the overall radial distribution of collagen filaments. It has been suggested that the postnatal synthesis of HA and the subsequent network swelling by unbound HA are the driving force for the splay deformation.135 The radial distribution of collagen II filaments in the mature eye does therefore reflect the translation of molecular order to the macroscopic level induced by a liquid-crystalline deformation mechanism.

Figure 19. Orientation of collagen II fibrils within the vitreous body of the human eye. In the vitreous cortex bundles of fibrils are firmly attached to the retina and oriented parallel to the cortex surface. Reproduced with permission from ref 132. Copyright 2000 IOP Publishing. All rights reserved.

The gel maintains the transparency of the media and supports the structures of the whole organ. The main components of the vitreous body include water (ca. 80%), type II collagen fibrils, and two polyanionic glycosaminoglucans: hyaluronic acid (HA) and chondroetin sulfate (CS). The sequence of assembling steps of these components was summarized (Figure 20) in the following manner.132−135 The first step is the stabilization of thin collagen II fibrils in the 10 nm diameter range through surface decoration with proteoglucans.132−134 A decorating proteoglucan is a nonfibrillar form of collagen (collagen IX) that can establish covalent links with collagen II (Figure 17) and with the polyanionic CS (Figure 20a).135,136 The proteoglucan has terminal sites (G1) able to form strong bonds with HA. It is important to remark that collagen II, collagen IX, and CS chains were observed during the early stage of the biosynthesis of the gel. The appearance of HA chains occurs during the postnatal increase of the volume of the vitreous cavity.132 The second assembling step involves the incorporation of decorated collagen II into a hyaluronic network (HAb) in which the network junctions are localized at the G1 terminal of the proteoglucan (Figure 20b). The final assembling step is the swelling of the network by more unbound HA (HAnet). The peculiar organization of the fibrillar component has been the object of unresolved debate.132 Figure 19 shows that fibrils

4.3. Nervous Tissue

Neurons are nerve cells that perform basic cellular processes such as protein synthesis and energy generation. However, at variance with other cells, neurons have specialized extensions that receive (dendrites) or transmit (axons) electrical impulses. Axons can be much longer than dendrimers, even approaching 1 m. They send signals to other neurons or muscles through axon terminals (synapses). The axons include an insulating myelin envelope based on concentric layers of lipids, phospholipids, and proteins. The sheath is occasionally interrupted (nodes of Ranvier) and allows high-resistance, low-capacitance electrical insulation coupled to the capacity of “saltatory conduction” from node to node. The structure of the conducting cytoskeleton filaments was recently established by Xu et al.137,138 Using a high-resolution fluorescence imaging technique (stochastic optical reconstruction microscopy) they evidenced that long actin filaments are oriented parallel to the long axis of dendrites (Figure 21a). However, in the case of the axons, rings of adducin-capped actin are connected by up to 10 spectrin tetramers and oriented with the long axis of the axon, as schematized in Figure 21b. Ankirin proteins anchor the actin−spectrin cytoskeleton complex to proteins in the insulating membrane. O

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that reinforces red blood cells).139 The second model (Figure 21d) assumes rings bound to spectrin tetramers: polymerization occurs by formation or more bonds between actin rings and spectrin tetramers.140 The difference between the corresponding association constants for a single-site bond may be significant and influenced by physiological conditions, but it is not the essential feature of the polymerization. The unique feature that applies to either type of repeating units is the establishment of up to 10 supramolecular bonds with the next unimer (F = 2, S = 10), which will enormously increase the overall binding constant K. For a single bond constant as small as 10 mol−1, K would be in the order 1010 when 10 sites are involved (section 3.2.1). According to eq 1, DP could attain the order of 105. The repeating units in Figure 21c and 21d have a length of ca. 200 nm, which essentially coincides with the length of the spectrin tetramer. Also on this basis, an axon about 1 cm long could attain a DP in the order of 105. Such large values are not unreasonable and lead to the suggestion that long axons can grow to macroscopic dimension without intermolecular cooperative effects (SLC, Supramolecular Liquid Crystallinity (SLC) in section 3.2.3). The actin−spectrin tubular complex in Figure 21b rather than the actin filaments (detailed in section 3.2.2) found in the dendrimers appears ideally suited for the design of the axon. Not only does the strong assembling mechanism allow the translation of its nanostructure to macroscopic dimensions but also a considerable rigidity to resist bending and other deformations is expected for tubular systems (i.e., the persistence length of microtubules attains values in the macroscopic range, cf. section 3.2.3). An independent evaluation of the binding constant and persistence length of

Figure 21. (a) Assembly of extended actin filaments within the dendrimers. Adapted with permission from ref 138. Copyright 2013. (b) Organization of the adducin-capped actin-spermicin complex in axons. Adapted with permission from ref 137. Copyright 2013. (c) Repeating unit formed by actin/adducin rings and dimeric spectrin. (d) Repeating unit formed by actin/adducing rings and spectrin tetramers.

Two types of supramolecular bonds occur at each binding site of the structure in Figure 21b: one between spectrin and the actin ring and one for the dimerization of spectrin. Correspondingly, the two repeating units schematized in Figure 21c and 21d may be considered. The first model (Figure 21c) assumes rings bound to spectrin dimers: polymerization occurs by the association of two spectrin dimers to form a spectrin tetramer (model proposed by Morrow et al. for the membrane

Figure 22. (a) Structural organization of myofibrils into sarcomeres, schematized on the basis of high-resolution optical microscopy. Dark bands (A) correspond to the overlap of thin and thick filaments. I bands include only thin filaments. Z lines mark the boundary of each sarcomeres. (b) Thin filament includes an actin double helix with bound tropomyosin and troponin that are the sites for switchable bridges with the thick filaments. Myosin double chains terminated by globular heads (sites for ATPase and anchoring to actin) associate in pairs with opposite orientation and assemble into the thick filament. (c) Contraction: six thin filaments are attracted toward the center of the sarcomere by the switchable bridges with the thick filament. (d) Electron microscopy image, taken on a section of contracted A band, supports the hexagonal organization of both components. Adapted with permission from ref 147. Copyright 2014 Creative Common Attribution License. P

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the assembly in Figure 21b is needed to put on a firmer basis the above preliminary conclusions. The mechanism used by neurons to direct axons to specific targets is defined as axon pathf inding and is under intense investigation. It is associated with a cone at the tip of the growing axon that has receptors which recognize guidance molecules such as cadherins (Ca-dependent cell adhesion proteins).141 The recognition of specific directional clues may be assisted by algorithmic processes such as those discussed in section 3.1.2.43

reversibly interpenetrate due to switchable interactions between them. Differences in the lattice organization of the thick filament occur in different vertebrates. The evolutionary and functional dependence of detailed lattice organizations were recently discussed.147 Growth. As done in the cases of the DNA−lipid system, we may describe the assembly mode of the present system in terms of separate contributions of longitudinal and lateral supramolecular polymerization. Considering the function of the skeletal muscle, we would expect longitudinal growth to be favored over the lateral one. A similar occurrence was verified for the growth of collagen fibrils when lateral growth became limited by the occurrence of lateral decoration (section 4.2.1). Results for the present system confirm that growth of muscle during development occurs by addition of successive sarcomeres. The thickness of a relaxed sarcomere remained unchanged in the order of 2.5 μm. To describe this system in terms of supramolecular polymerization of whole cells we need to identify a repeating unimer and the contact forces along the myofibril axis. The sarcomere, a strongly asymmetrical cell, appears to be a suitable unimer. For the evaluation of the binding energy one should know the detailed structure at the Z lines. The connection between adjacent sarcomeres appears to involve a filament of one sarcomere linked to four filaments of the following one and the intervention of the two proteins α-actinin and tinin.142 The latter protein could establish a continuous link through subsequent sarcomers. Assuming upper lengths of 30 cm for a typical myofibril and 3.0 μm for the sarcomere,148 a maximum DP in the order of 105 might be attained, suggesting a large association constant in terms of the MSOA mechanism (eq 1). However, it is not clear that the above assembling scheme of the macroscopic myofibril provides a large number of sites, as was instead observed in the case of the neural axon (section 4.3).

4.4. Muscle Tissue

There are three distinct types of muscle cells in vertebrates: skeletal, controlling voluntary movements; cardiac, pumping blood from the heart; smooth, responsible for involuntary movements of organs such as blood vessels. A skeletal muscle is composed of bundles of long, cylindrical, and multinucleated cells called myofibers (or muscle fibers). Each myofiber includes several myof ibrils composed by a sequence of interdigitating thin actin (7 nm diameter) and thick (15 nm diameter) myosin filaments. Electron microscopy and low-angle X-ray diffraction images reveal the occurrence of dark (A) and light (I) bands separated by Z lines (actually flat disks). The latter mark the boundaries of a repeating unit called sarcomere, which includes one A band plus two halves of the adjacent I bands (Figure 22a).142−145 The actin filaments are anchored (Figure 22b) to the Z lines and include minor component proteins (tropomyosin and troponin) that have binding sites for neighboring myosin molecules that are formed by two linear chains and two globular heads (Figure 22b). The myosin heads point toward the actin filaments and include sites for binding to it and for ATPase.136 The myosin filament is formed by several antiparallel dimers of myosin molecules. Elastic filaments made of the long protein titin (1 nm diameter) assist the permanence of thick filaments at the center of the sarcomere and the recovery of the resting state following contraction. Contraction. Under stimulation by motor neurons, calcium ions are released by the cell sarcoplasmatic reticulum (membrane-bound microtubules surrounding myofibrils) and bind to troponin, inducing movement of tropomyosin and exposing binding sites for actin−myosin interaction. The ensuing contraction occurs due to the interdigitation (sliding) of thick and thin filaments, as more bridges are established between the heads of the thick and the sites on the thin filaments.146 An opposite orientation (polarity) of actin filaments in the two halves of the sarcometer is required. During relaxation, calcium ions migrate back to the sarcoplasmatic reticulum, the bridges between the two filaments weaken, and the system returns in its rest configuration, ready for a new cycle. The scheme in Figure 22c indicates that six thin filaments surround each thick filament. The scheme refers to the central hexagon within the overall distribution of the components illustrated in Figure 22d. The hexagonal distribution of the two components is supported by electron microscopy/small-angle X-ray images of myofibril sections taken in the A band (where the two types of filaments are interdigitated), in the I band, and close to the M line.147 The hexagonal scheme has similarities with the scheme earlier discussed in connection with DNA− lipid assemblies (section 3.2.5). From a structural standpoint, the ability of skeletal muscle to undergo contraction cycles rests on the occurrence of two distinct hexagonal structures that

5. ENGINEERED ASSEMBLIES Cells synthesize biological polymers, a role that parallels that of the organic chemist who synthesizes polymers. A variety of cell types can be used to direct the formation of particular tissues. Stem cells of the embryonic type (ES) are “pluripotent” because have large proliferation rates and can be differentiated into specialized cells for the production of most tissues (muscle cells, nerve cells,...), although the uniform differentiation to a single tissue type may be problematic. Adult (somatic) stem cells can only be differentiated into various cell types of the organ from which they originate. The induced pluripotent stem cell (iPS) discovered by Takahashi and Yamanaka are somatic cells that have been genetically reprogrammed to an ES state by reactivating the expression of specific genes.149 Formed cells respond to chemical signals from neighboring cells and also to signals from the matrix and from mechanical deformation (“cells know what to do”). Sato and Clevers recently reported the behavior of intestinal stem cells in vitro (a culture resembling the in vivo counterpart). They observed the formation of self-assembled miniguts (epithelial small tubes in the alimentary canal) that are quite similar to those formed by the living organism.150 The possibility that specialized stem cells can spontaneously reproduce the native organs would have important applications in regenerative medicine. Biosynthetic implants are devices artificially created by growing, over manmade substrates, cells able to restore or Q

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replace damaged tissues.151 Scaffolds were originally produced using a variety of natural (i.e., collagen) or synthetic (i.e., polylactic acid) materials casted with suitable 3D shapes and compatible with the tissue to be regenerated in vivo. Electrospinning152 has been considered for the formation of scaffolds with a fine texture similar to that of the natural tissue matrix. Tissues that do not require significant vascularization (i.e., skin) were successfully produced. More recent scaffolds have used connective tissue in which all cellular components were eliminated. The decellularized scaffolds retained the macro- and nanoarchitecture of the original tissue.153 Investigators in Sweden recently reported the decellurization of a complete organ (porcine heart) that retained integrity in its mechanical properties and in the components (collagen, elastin, glycosaminoglycans) of its extracellular matrix.154 More recent progress in this interdisciplinary area includes attempts to engineer a vascularized network. The vascularization problem is particularly important in tissues that include layers of cell (thicker than ca. 100 μm) that need to receive their vital fuel, oxygen and nutrients, from the tiny vessels of the vascular system. The engineered construction of perfusable vascular networks was attempted using different strategies. Cuchiara et al. reported a multilayer soft lithographic fabrication approach for several systems of biological interest that included channels allowing solute diffusion and cell viability.155 Among other methods, microgrooves were imprinted on a suitable substrate by molding on it a 3-D lattice of rigid filaments which was later sacrificed (dissolved).156 Figure 23 represents a microchannel architecture imbedded in an epoxy matrix that mimics ivy leaf venation.157 The

6. CONCLUDING REMARKS There is a substantial correlation between the various classes of self assembling systems considered here with regard to strategies for the translation of molecular order to macroscopic dimensions. In the case of low molecular weight materials and covalent flexible polymers, the main concern was the removal of structural defects such as dislocations and chain entanglements. For rigid polymers, high molecular weight and conformational rigidity induced the orientational field of liquid crystallinity that promoted the translation of molecular order to macroscopic dimensions. In the case of supramolecular polymers, the dynamic nature of the structure reduces the impact of chain entanglements, but the need to increase growth and orientation persists. Enhanced growth was mostly pursued using chemical strategies such as large binding constants, small dissociation rates, and cooperative effects. Enhanced orientation was pursued exploiting the orientational field of liquid crystallinity and growth over templates or formed structures. Liquid crystallinity was again induced by conformational rigidity. However, at variance with conventional polymers, supramolecular liquid crystallinity also has a direct role in enhancing polymerization. As a result, not only binding constants but also particularly large persistence lengths are expected to be the main driving forces for an efficient translation of molecular order to macroscopic dimensions. In the case of cell-driven biopolymers that do attain order over macroscopic dimensions, the above expectations were verified. Microtubules and axons are indeed characterized by the largest values of persistence length and binding constants so far reported. Intermediate values of persistence length and association constants, as in the case of actin, only allow growth to the mesoscopic range.57,61 Relatively simple assemblies of whole cells, such as planar epithelium and striated muscles, exhibited features consistent with the establishment of positional and orientational order. However, complex shapes and templates evidence the difficulty in describing the natural formation of organs using basic assembly principles. Carving and remodeling of basic structures must thus be attributed to the multiplicity of control signals from the biochemical machinery. The material scientist interested in reproducing the outstanding length and rigidity of the axon filament might consider the synthesis of ring structures having a variable number of sites for supramolecular bonds. An intermediate columnar organization may occur. Saturation of the supramolecular bonds with rigid tie molecules linking consecutive rings (scheme c and d in Figure 21 and TOC) may promote the formation of a tubular structure. Determination of the degree of polymerization and persistence length as a function of the number of tie molecules would provide a quantitative assessment of the assembling mechanism. The description of complex assemblies in terms of supramolecular polymerization mechanisms represents an “alternative” approach to the description of complex structures. One of several examples was the description of DNA−lipid assemblies (Figure 13b) in terms of a complex of DNA coated by the charged head of the lipid and the association of this complex by interdigitation of the hydrophobic tails. A relevant question is how does the description in terms of supramolecular polymerization add to what is or may be known from the experimental or theoretical assessment of a specific structure? The experimental determination reveals “how” a

Figure 23. Engineered tissue. Fluorescent image of microchannels embedded in epoxy matrix. Reproduced with permission from ref 157. Copyright Royal Society of Chemistry.

microvascular network was obtained by depositing fugitive organic ink to the desired pattern (direct writing technique), infiltrating with epoxy resin, curing, and finally removing the fugitive ink. The authors report that fluid transport was optimized when the dimensions of primary and bifurcated channels (spanning from 50 to 250 μm) obeyed a rule established by the botanist Cecil Murray in 1926.158 The decellularized scaffolds may have growths with smaller diameters. Seeded epithelial cells proliferated along the preferential direction forming nanotubes within a prepatterned network. R

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ACKNOWLEDGMENTS The author expresses his appreciation to Profs. Alvin Crumbliss, David Sherwood, Steven Baldwin, and Stephen Craig at Duke University and to Prof. Mario Pestarino at University of Genoa for illuminating discussions and useful advice. Great appreciation is also manifested to Prof. Virgil Percec for the invitation to contribute to this special issue of Chemical Reviews, to the DISTAV Department of the University of Genoa for hospitality during the Fall Semester of 2014, and to Cinzia Bongianni and Emilee Renk for the elaboration of the illustrations.

specific structure is organized; the polymerization mechanism reveals, in general thermodynamic terms, “why” the structure grew. Moreover, the latter approach has some predictive features (e.g., the DP) and does suggest useful assembly strategies to the biologists and material scientists who are expanding the frontiers of nano- to macrotechnology. In addition to the complex biochemical machinery that controls the development and maintenance of in vivo tissues, other biochemically induced transformations control the functioning of biological systems. For instance, motility and force generation by actin filaments are known to be driven by coupling of chemical reactions (ATP hydrolysis) to morphological transformations and assembling−disassembling processes.159,160 The design of functional systems mimicking such biological functions is in rapid expansion. Needed network models for handling the complexity of multiple interactions and the selectivity of algorithmic recognition may emerge from the areas of systems biology and systems chemistry.161,162

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AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest. Biography

Alberto Ciferri received his Doctoral degree in Physical Chemistry from the University of Rome. He was a postdoctoral fellow with H. Benoit in Strasbourg and with P. J. Flory in Pittsburgh and worked for about 10 years at the Chemstrand Research Center in the Research Triangle Park of North Carolina. Under invitation from G. Natta, he returned to Italy to head a new institute for polymer science of the National Research Council. He became a Professor of Macromolecular Science at the University of Genoa, from which he has now retired, and has maintained an association with Duke University from 1975 to the present time. He has been active in fundamental areas of polymer science, notably network elasticity, fibrous proteins, ionic interaction, liquid crystallinity, and supramolecular assemblies. He has published over 200 papers and edited several pioneering books in the above areas to which several outstanding scientists have cooperated. He has received numerous visiting professor appointments, including Caltech, the University of Kyoto, the Weizmann Institute, and the Academy of Science of the USSR. He established the Swiss-based Jepa-Limmat Foundation that promotes advanced education in developing countries, notably in Central America and Central Asia. For his work he received honorary doctoral degrees. S

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