Search tips
Search criteria 


Logo of hfspjLink to Publisher's site
HFSP J. 2010 February; 4(1): 26–40.
Published online 2010 January 14. doi:  10.2976/1.3267779
PMCID: PMC2880027

How protein materials balance strength, robustness, and adaptability


Proteins form the basis of a wide range of biological materials such as hair, skin, bone, spider silk, or cells, which play an important role in providing key functions to biological systems. The focus of this article is to discuss how protein materials are capable of balancing multiple, seemingly incompatible properties such as strength, robustness, and adaptability. To illustrate this, we review bottom-up materiomics studies focused on the mechanical behavior of protein materials at multiple scales, from nano to macro. We focus on alpha-helix based intermediate filament proteins as a model system to explain why the utilization of hierarchical structural features is vital to their ability to combine strength, robustness, and adaptability. Experimental studies demonstrating the activation of angiogenesis, the growth of new blood vessels, are presented as an example of how adaptability of structure in biological tissue is achieved through changes in gene expression that result in an altered material structure. We analyze the concepts in light of the universality and diversity of the structural makeup of protein materials and discuss the findings in the context of potential fundamental evolutionary principles that control their nanoscale structure. We conclude with a discussion of multiscale science in biology and de novo materials design.

Strength, robustness, and adaptability are properties of fundamental importance to biological materials and structures and are crucial to providing functional properties to living systems. Strength is defined as the maximum force (or pressure) a material can withstand before breaking. Robustness is defined as the ability of a material to tolerate flaws and defects in its structural makeup while maintaining its ability to provide functionality. Adaptability refers to the ability of a material to cope with the changing environmental conditions. These properties are crucial for materials in biology (such as skin, bone, spider silk, or cells), which either provide structural support themselves (such as the skeleton formed by bone) or need to withstand mechanical deformation under normal physiologic conditions (such as cells and tissue associated with blood vessels that are exposed to the pressure of the blood).

In engineering, strength and robustness are often disparate properties as it remains challenging to create materials that combine these two features. Glass or ceramics, for example, are typically very strong materials. However, they are not very robust: even a small crack in a glass or an attempt to deform glass considerably will lead to catastrophic failure. In contrast, metals such as copper are very robust; however, they do typically not resist large forces (Courtney, 1990). Yet, these materials allow for large deformation and even the existence of cracks in the material does not lead to a sudden breakdown. In contrast, many biological materials (such as cellular protein filaments, blood vessels, and collagenous tissues such as tendon, spider silk, bone, tendon, and skin) are capable of providing both properties—strength and robustness, very effectively, and also combined with the ability to adapt to changes in the environment (Fratzl and Weinkamer, 2007; Meyers et al., 2008). For example, blood vessel tissues comprised of cells (endothelial and smooth muscle cells) and extracellular matrix protein material secreted by these cells, together from a highly elastic tissue material that is capable of withstanding hemostatic pressure variations, and moreover, is capable of adapting to changes in functional requirements by forming new tissue or removing tissue no longer needed. For example, the activation of angiogenesis (the formation of new blood vessels) occurs in response to physiologic cues where an increase in nutrient and oxygen is required (such as development of the embryo, ischemic wound sites, ovulation, etc.) in order to support newly formed tissue or to assist in wound healing (Folkman, 2003). Extracellular matrix materials such as collagenous tissues or elastin fibers represent another example of highly adaptive materials that shows great resilience to environmental changes, self-healing ability, as well as deformability and strength (Fratzl, 2008). Other examples for biological systems in with hierarchical features include gecko adhesion mechanisms, where extremely strong and robust adhesion is reached through the use of weak van der Waals interactions (Autumn et al., 2002; Arzt et al., 2003; Gao et al., 2005).

Most fibers, tissues, organs, and organisms found in nature show a highly hierarchical and organized structure, where features are found at all scales ranging from protein molecules (≈50 Å), protein assemblies (≈1–10 nm), and fibrils and fibers (≈10–100 μm) to cells (≈50 μm) and to tissues and organs (≈1,000 s and more μm, Alberts et al., 2002; Vollrath and Porter, 2006; LeDuc and Schwartz, 2007; Rammensee et al., 2008). In recent years, the study of the role of these distinct hierarchical structures, how they regulate the growth and function of biological systems and what the driving forces are for their formation, have emerged as an active field of research referred to as materiomics. Most early studies have focused on investigations at single scales, or treated tissues or the cellular microenvironment as a continuum medium without heterogeneous structures (e.g., studies that examine the isolated effects of material stiffness or the role of chemical cues alone on cell behavior). However, the cause and effect of biological material mechanics is likely more complex than a singular input at a specific scale, and thus, the examination of how a range of material scales and hierarchies contribute to certain biological function and dysfunction has emerged as a critical aspect in advancing our understanding of the role of materials in biology in both a physiological and pathological context. Specifically, the origin of how naturally occurring biological protein materials are capable of unifying disparate mechanical properties such as strength, robustness, and adaptability is of significant interest for both biological and engineering science, and has attracted significant attention. To investigate these issues, this article provides a review of recent work and future challenges in this field. Specifically, we discuss here the key role that multiscale mechanics plays in defining a material’s ultimate response at failure and how nature’s structural design principles define the hierarchical makeup of biological materials. This process, likely evolutionarily driven, enables biological materials to combine disparate properties, such as strength, robustness, and adaptability, and may explain the existence of universal structural features observed in a variety of biological materials across species. Figure Figure11 shows a summary of the structural makeup of three example protein materials: intermediate filaments (an intracellular protein material), collagenous tissue (an extracellular protein material), and amyloids (an ectopic protein material), revealing their hierarchical structures that range from nano to macro. Table Table11 provides a summary and definitions of key properties and terms used in this article.

Table 1
Definition of major terms used in this article.
Figure 1
Hierarchical structure of three example biological protein materials, intermediate filaments (panel A), collagenous tissues (panel B), and amyloids (panel C).

To illustrate the key material concepts in a specific case, much of our discussion is focused on a particular protein material, intermediate filaments—a protein part of the cell’s cytoskeleton—and alpha-helical protein structures that form the basic constituent of this class of protein filaments. We begin with a brief review of this class of protein material. The cell’s cytoskeleton plays a crucial role in determining the overall cellular mechanical and biological properties. It consists of three major protein networks, actin, microtubules, and intermediate filaments (often abbreviated as IFs). Thereby, actin filaments and microtubules, both made up of globular proteins, are responsible for cell dynamics and motility as well as particle transport (Weitz and Janmey, 2008). However, these networks are rather brittle and break either at relatively low stress or low strains lower than 50% (Janmey et al., 1991). The third component of the cell’s cytoskeleton is an alpha-helix based intermediate filament protein network. In contrast to actin filaments and microtubules, intermediate filaments withstand much larger strains of up to several hundred percent (Fudge et al., 2008; Kreplak et al., 2008; Qin et al., 2009a). Intermediate filaments also form the structural basis for lamin intermediate filaments, which constitute an important part of the cell’s nuclear membrane (Sullivan et al., 1999; Dahl et al., 2004; Lammerding et al., 2004; Houben et al., 2007; Dahl et al., 2008). Similar to intermediate filaments in the cell’s cytoskeleton, lamin intermediate filaments fulfill the roles of defining the mechanical properties of the nuclear membrane and also participate in gene regulation (Sullivan et al., 1999; Dahl et al., 2004; Lammerding et al., 2004; Houben et al., 2007; Dahl et al., 2008). Their mechanical role has been demonstrated in several studies, which includes analyses of disease mechanisms in the rapid aging disease progeria (Dahl et al., 2006). The hierarchical structure of lamin intermediate filaments features a cascaded hierarchical structure that ranges from the scale of individual H-bonds to the scale of individual cells. Figure Figure1A1A shows a schematic representation of the different levels associated with lamin intermediate filaments. The alpha-helix based protein dimer structure is highlighted as well.


The paper consists of four major sections that cover different scales and aspects related to the issues of strength, robustness, and adaptability of protein materials. First, we present a section focused on strength and robustness of individual protein filaments. Second, we present a section dedicated to the analysis of hierarchical protein networks, spanning the scales from individual protein domains to micrometer sized networks. The discussion continues in a third part focused on a review of how adaptability is achieved in biological materials, illustrated based on the example of angiogenesis (blood vessel formation). The paper concludes with a discussion on universality and diversity of the structural makeup of protein materials in part four.

Deformation and failure of protein filaments

This section is focused on strength and robustness of individual protein filaments as they appear in a variety of protein materials (see Fig. Fig.1).1). The ultrastructure of protein materials such as intermediate filaments, spider silk, muscle tissue, or amyloid fibers universally consists of alpha-helix and beta-sheet structures as well as other universal structural motifs such as triple helical collagen molecules. These material components are unique in their making as they employ not only covalently bonded polypeptide chains but also H-bonds that give rise to unique folds and nanostructural arrangements of proteins by forming intramolecular as well as intermolecular contacts. Notably, H-bonds are intermolecular bonds, which are 100–1000 times weaker than those typically found in ceramics or metals. Due to the low bonding energy, individual H-bonds behave like liquids since their weak interactions can be disrupted even due to moderate thermal fluctuations. This is evident in water, for example, where a network of H-bonds exists that is established between individual water molecules. Yet, materials such as spider silk, intermediate filaments, and muscles display great mechanical resistance against deformation and failure. The key questions addressed here are: (1) How can mechanically weak structural elements such as proteins stabilized by H-bonds provide the basis to strong materials? (2) What role do hierarchical structures play in providing overall strength and robustness properties of a material?


We first address the question of mechanical strength of H-bonds by combing a chemical and mechanical perspective in the analysis. The key hypothesis considered here is that in order to understand the mechanical strength of H-bonds, it is essential to consider the effect of structural organizing of H-bonds on their effective properties. Indeed, H-bonds in naturally occurring protein motifs often display a high level of structural organization of H-bonds. Based on theoretical and computational molecular dynamics studies (Ackbarow et al., 2007; Keten and Buehler, 2008a,b) and experimental validation (Keten and Buehler, 2008b), the strength properties of clusters of H-bonds of different sizes were investigated based on a simple model system in which a single beta-strand with varying number of H-bonds was examined. Figure Figure2A2A shows the strength of clusters of H-bonds as a function of the size of the strand, characterized by the number of H-bonds (results obtained under quasistatic deformation at asymptotically vanishing deformation rates). Here the strength is defined as the maximum force required in order to initiate the breaking of the cluster, which is divided by the sheared area.

Figure 2
Size effect associated with clusters of H-bonds (Ackbarow et al. 2007; Keten and Buehler 2008a,b).

The results display interesting characteristics. First, as expected based on our knowledge of the weakness of individual H-bonds, the mechanical strength of individual H-bonds is zero. This observation is in agreement with the fact that water is a liquid and not a solid. Second, the analysis reveals that as the number of H-bonds in a cluster is increased, the strength increases as well, reaching a peak at Ncr≈3–4 H-bonds, achieved when all H-bonds in a beta-strand work cooperatively (for longer strands, localization of shear occurs similar to dislocations in metals, preventing a further increase in strength). Notably, the peak maximum strength is close to 200 MPa, resembling the shear strength of metals (Keten and Buehler, 2008a). These results show that the maximum mechanical strength is reached at a critical length scale, providing a strategy to overcome the intrinsic limitation of the weakness of H-bonds. It is noted that the H-bond energy itself depends on the solvent environment, which is reflected in changes in the energy barrier associated with breaking H-bonds. This effect is responsible for the variation in H-bond energies from 2–8 kcal/mol in various protein materials and solvent environments. Notably, the effect of these solvent induced variations in the H-bond energy have only a relatively small effect on the scaling behavior of the strength as reviewed above, as discussed in more detail (Keten and Buehler, 2008a). Specifically, the shape of the scaling as presented here and the fact that the maximum strength is reached at a critical number of H-bonds appears to be a universal feature.

Next we examine the robustness of a cluster of H-bonds, again for different geometries. Robustness is a key measure that reflects the ability of a system to deal with changes in the environment or changes in its structural makeup (e.g., loss of bonding in parts of a protein, crack formation, etc.). The robustness R is defined as the strength F of a filament in which one element (here, one H-bond) is missing, divided by the strength of an intact filament


[the number of H-bonds in a cluster refers to the number of H-bonds in a turn as shown in Fig. Fig.3A].3A]. The results for the robustness as a function of the number of H-bonds are plotted in Fig. Fig.2A.2A. The graphs show that the robustness increases continuously with the number of H-bonds (Ackbarow et al., 2007). However, the actual increment of robustness due to adding one H-bond decreases with the number of H-bonds. Specifically, it is found that a robustness value close to 100% reached at a size of 3–4 H-bonds, perhaps resembling a balance between optimal material use and strength. The 100% robustness value can be explained by the fact that beyond the critical number of H-bonds Ncr, the strength does not change with the number of H-bonds, that is, F(i)=Fmax for i[gt-or-equal, slanted]Ncr.

Figure 3
Strength-robustness relation for alpha-helical protein filaments [results adapted from Keten and Buehler (2008a), Ackbarow and Buehler (2009a), and Qin et al. (2009a)].

This result illustrates that by utilizing a size effect that is rooted in a fundamental scaling of the strength as a function of the geometry, the intrinsic limitation of H-bonds, their mechanical weakness, can be overcome while maintaining a relatively high level of strength and robustness. Considering a variety of protein structures found in nature, we find that the size of H-bond clusters in most proteins is close to the critical number Ncr associated with maximum mechanical strength, as shown in Fig. Fig.2B.2B. Therefore, the occurrence of a strength peak at this characteristic dimension provides a possible explanation for the geometric features of several protein constituents. Possibly, the clustering of H-bonds into small groups could be a universal evolutionary principle guided by the requirement to present mechanically strong and robust building blocks to form a diverse group of fibers and tissues. This concept may explain the universal nanostructural structural principle found in a diverse set of protein materials. Furthermore, the structure formed by “soft” H-bond clusters, sandwiched between “stiff” polypeptide amino acid chains, resembles a common design principle used in the construction of brick walls used in civil engineering for centuries at the macroscale [see inlay in Fig. Fig.2A].2A]. Future studies are needed to put these concepts into a more solid footing in the context of evolutionary science.


We now proceed with a study of strength-robustness properties of filaments composed out of different hierarchical assemblies of alpha-helical protein domains (Keten and Buehler, 2008a; Ackbarow and Buehler, 2009a; Qin et al., 2009a). The basic building block for all filaments considered in this case study is an alpha-helical protein domain as shown in Fig. Fig.3A,3A, stabilized by 3–4 H-bonds per turn (an alpha-helical turn has an average of 3.6 H-bonds (Alberts et al., 2002). For this particular geometry the mechanical resistance (both strength and robustness) of the individual protein domain is at its maximum, as shown in Fig. Fig.2A.2A. The question examined here is to find out whether or not it is possible to build larger-scale structures out of individual protein domains that maintain high levels of strength and robustness.

In this analysis, the concept of robustness is defined as the strength of an intact filament divided by the strength of a filament in which one element (here, one alpha-helix) is missing at the smallest level [following the definition provided in Eq. 1]. To explore the effect of structural variations in the performance in the strength-robustness domain, we consider eight alpha-helices and arrange them in all possible geometries and measure their properties. Figure Figure3B3B depicts the geometries and results for eight alpha-helices (the definition of subelements and their arrangement are those shown in the inlay of the figure). The analysis shows that even though no additional material is used, the mechanical performance changes significantly as the hierarchical arrangement of the structure is varied (see caption of Fig. Fig.33 for details regarding the nomenclature). The {8} structure provide very high levels of robustness, albeit at low strength. In contrast, the {4,2} structure provide high strength albeit at low robustness. However, there are some structures that provide an optimal combination of both properties, {2,2,2} and {2,4} structures. Among these, the {2,4} structure is the best performer as it provides the highest levels of strength and robustness. The {2,4} structure represents a fiber composed of two bundles of fourfold coiled-coil alpha-helices (CC4) (Ackbarow and Buehler, 2009a).

The analysis is extended by considering a much larger number of filaments. As in the earlier study with only eight elements, the elements are assembled in all possible hierarchical structures and tested for their strength and robustness. Figure Figure3C3C depicts results for 16,384 alpha-helices (Qin et al., 2009a), where an analysis of the distribution of structures and their performance shows that most structures (>98%) in Fig. Fig.3C3C fall onto a curve referred to as the banana-curve, where strength and robustness are mutually exclusive properties. Only ≈2% of all structures lead to high strength and high robustness.

The investigation shows how high-performance materials can be made out of relatively weak constituents such as alpha-helices that are bonded by structurally and mechanically inferior H-bonds and by arranging them into specific hierarchical patterns. The resulting robustness-strength plots suggest a similar behavior as that found in many biological materials, as indicated in Fig. Fig.3C,3C, in that they combine disparate properties. The particular distribution of performance characteristics for a large number of elements may explain why most engineered materials (such as metals, ceramics, glass, etc.) show a poor performance of strength and robustness. This is because most randomly picked arrangements fall on the banana curve (>98%). Engineered materials often show this behavior since hierarchical nanostructural geometries have not yet been utilized engineering materials design. In contrast, biological materials may have achieved the particular high performance structures through the adaptation of hierarchical structures. These observations suggest that the structure of biological materials may have developed under evolutionary pressure to yield materials with multiple objectives, such as high strength and high robustness, a trait that can be achieved by utilization of hierarchical structures. Further exploration of this concept in both experimental and theoretical studies could shed further light into these mechanisms.

Deformation and failure of protein networks: An issue of multiple scales

We now focus on other types of assemblies of proteins, and discuss structures that form hierarchical network structures at levels far beyond a single filament. In literature, most protein materials have been studied either from a macroscale perspective (e.g., through continuum models) or from a single-molecule level but not from an intermediate “mesoscale” viewpoint. For example, alpha-helix based intermediate filament networks have been investigated through shear experiments of protein gels (Janmey et al., 1991) as well as through in situ studies with particle tracking rheology (Sivaramakrishnan et al., 2008), where their material properties have been explored from a macroscopic perspective. On the other hand, the mechanical properties of the elementary nanoscale alpha-helical building blocks were studied extensively and several publications have reported advances in the understanding of their nanomechanical behavior from both experimental (Lantz et al., 1999; Kageshima et al., 2001) and theoretical (Ackbarow and Buehler, 2007;Ackbarow et al., 2007; Buehler and Ackbarow, 2007;Buehler et al., 2008; Ackbarow et al., 2009c; Qin et al., 2009b) perspectives. A more complete understanding of properties such as strength, robustness, and adaptability, however, requires us to take a mesoscale perspective that considers all scales and the hierarchical structures from nano to macro.

Here we review studies of a simple model system of a hierarchical protein material, as shown in Fig. Fig.44 (Ackbarow et al., 2009b). The model is designed with the objective in mind to devise a simple physics based representation of an intermediate filament network in the nuclear envelope [lamina, further details on the simulation setup, results, and interpretation are included in Ackbarow et al. (2009b)]. The goal is to elucidate the key parameters of interactions between structure and properties at multiple hierarchical levels without attempting to provide a quantitative model of this particular protein material. A lattice structure, resembling the meshwork arrangement of intermediate filaments in the nuclear envelope is subjected to tensile loading as shown in Fig. Fig.5A5A (upper left plot). To model the effect of the existence of structural flaws on the material performance, we insert a cracklike defect in the center of the sample, as highlighted with the white ellipsoid. This setup serves as a simple model to mimic the existence of structural irregularities as shown in Fig. Fig.44 (nuclear envelope level H5; marked in white color). The protein network itself is modeled based on a coarse-grained bead-spring network as highlighted in Fig. Fig.5A5A (upper inlay), following a multiscale modeling approach. Each of the one-dimensional chains resembles an alpha-helix based protein filament and serves as a simple model representation of an intermediate filament protein. All parameters in the coarse-grained model are derived from full-atomistic simulations, which have led to the characteristic three-tiered elastic-softening-stiffening response of alpha-helical filaments [see inlay in Fig. Fig.5A].5A]. The first regime resembles the initial stretching of the filament without rupture of H-bonds, that is, elastic deformation. Regime β resembles the secondary regime of stretching, a very soft plateau, during which the protein filament unravels by unfolding of alpha-helical turns with a slight increase of the force as the strain is increased [which occurs by rupture of individual alpha-helical turns as shown in Ackbarow et al. (2007)]. Regime γ resembles the stiffening regime during which the protein filament’s stiffness increases manifold due to stretching of strong bonds (covalent bonds).

Figure 4
Hierarchical structure of a simplistic model of the intermediate filament protein network in cells [figure adapted from Ackbarow et al. (2009c)].
Figure 5
Deformation field of the protein network [plot adapted from Ackbarow et al. (2009c)].

We begin our analysis with carrying out a tensile deformation test of the protein network. We carry out a detailed analysis of the deformation mechanism, as shown in Fig. Fig.5A,5A, where the color of the alpha-helical filaments indicates how much it has been deformed (identifying the three regimes: α, β, and γ as described above). At small deformation, the protein filaments start to unfold as H-bonds begin to rupture and the alpha-helical proteins uncoil, turn by turn [Fig. [Fig.5A,5A, snapshot II]. At small to moderate deformation, the deformation mechanism of the network is characterized by molecular unfolding of the alpha-helical protein domains, leading to the formation of very large yield regions. This is shown in Fig. Fig.5A5A (snapshots III and IV) where the yield regions appear first in yellow and then in red color. These yield regions represent an energy dissipation mechanism to resist catastrophic failure of the system (referred to as “dissipative yield regions”). Rather than dissipating mechanical energy stored in the material due to the external strain by breaking of strong molecular bonds as it would happen in a brittle material like glass or a ceramic, the particular structure of alpha-helical proteins makes it possible that mechanical energy is dissipated via a benign and reversible mechanism, the breaking of H-bonds. Catastrophic failure of the structure does not occur until a very large region of the structure has been stretched so significantly that the strong bonds within and between alpha-helical protein filaments begin to fail. As shown in Fig. Fig.5A5A through the highlighted crack shape, we observe that the formation of yield regions enables a significant change in the shape of the crack, from an initial ellipsoidal shape where the longest axis points in the x-direction (horizontal orientation) to an ellipsoidal shape where the longest axis points in the y-direction (vertical orientation).

This microscopic change in the crack shape induced by the macroscopic applied load has important implications on the failure behavior of the system and provides an intrinsic mechanism to mitigate the adverse effects of the flaw. A simple approximation of stress fields at a crack tip can be obtained using the Inglis solution for elliptical cracks (Lawn, 1993, see schematic in Fig. Fig.5B5B with explanation of variables), where the crack tip stress is given by


In Eq. 2, σtip (=σyy at the crack tip) and σ0 are the stresses at the crack tip and the far-field, respectively and ξ and δ are the x- and y-axes lengths of the elliptical crack shape before failure. Specifically, the parameters ξ and δ describe the transformed crack geometry after blunting has occurred through formation of large yield regions mediated by protein filament stretching but before the final stage of deformation has begun. We note that the parameters ξ and δ describe the initial crack geometry at the beginning of the simulation, before the transformation has occurred. Equation 2 can be used to make a few interesting predictions. The equation provides a simple model for the reduction in stress magnification at corners due to structural transformation as discussed above. For an ellipsoidal crack shape where the longest axis points in the x-direction, the ratio ξ[dbl greater than]1 (Fig. (Fig.5B,5B, left), the stress at the tip is much larger (σtip[dbl greater than]σ0) than for an ellipsoidal crack shape where the longest axis points in the x-direction, the ratio ξ<1 [Fig. [Fig.5B,5B, right], where σtip is only slightly larger than σ0. For example, for the geometry discussed here the initial ratio ξ/δ≈5, leading to σtip=11σ0. After the crack shape transformation has occurred, ξ≈0.3, leading to σtip=1.9σ0, reduced by a factor of ≈6.

The analysis of the protein network reviewed here shows that the cascaded activation of deformation mechanisms at multiple scales enables the material to tolerate structural flaws (cracks) of virtually any size. This unique behavior is in stark contrast to engineered materials (e.g., metals or ceramics; materials constructed with no hierarchies), where the presence of cracks leads to a severe reduction in strength and is the most common cause for catastrophic materials failure (Broberg, 1990). Materials failure typically initiates at locations of peak internal material stress at the corners of cracks), where atomic bonds are likely to break, leading to the propagation of fractures. Table Table22 provides a summary of the roles and mechanisms of individual levels of structural hierarchies shown in Fig. Fig.55 for the overall system behavior, illustrating that each hierarchical level plays a key role in achieving the overall system performance. The detailed deformation and failure mechanism is summarized as follows:

  • Initially, the system is loaded in Mode I (tensile load), with the load applied vertically to the long axis of thecrack. In solids, this represents the most critical mode of loading with respect to inducing high local stresses in the vicinity of the crack tip.
  • As the load is applied, the protein filaments start to unfold as H-bonds begin to rupture and the alpha-helical proteins uncoil [see blowups in Fig. Fig.5A5A].
  • The system elongates in the loading direction, and the shape (morphology) of the crack undergoes a dramatic transformation from mode I to a circular hole to finally an elongated crack aligned with the direction of loading [see Fig. Fig.5A].5A]. This transformation is caused by the continuous unfolding of the individual proteins around the crack, which can proceed largely independently from their neighbors.
  • As discussed based on the simple analysis derived from Inglis’ solution, the elongated crack features very small stresses in the vicinity of the crack. The transformation of the crack shape is thus reminiscent of an intrinsic ability of this material to provide self-protection against the adverse effects of the existence of cracks.
  • The almost identical strain at fracture regardless of crack size is due to the similar stretching mechanism and unfolding of the proteins at the initial stages of loading. Due to the self-protection mechanism and the related change in the crack shape (that is, the alignment along the stress direction) the crack becomes almost invisible, even if dominating large parts of the cross-sectional area, and has little adverse effect on the overall system performance.
Table 2
Role of hierarchical levels in the deformation and failure behavior of alpha-helical protein network (see Fig. Fig.44 for schematic of the structure considered here, Ackbarow et al. 2009c).

These investigations provide insight into the fundamental deformation and failure mechanisms of an abundant class of biological materials that feature networks of similar protein filaments. Specifically, the results may explain the ability of cells to undergo very large deformation despite irregularities in the structural makeup of the protein network. More generally, the concepts identified here may also apply to many other protein materials, and suggest that the controlled structure formation at multiple levels could be the key to obtain an integrated performance that combines disparate properties. Overall, intrinsic mechanisms such as the flaw-tolerance mechanisms revealed in the protein network present an intriguing ability of this class of materials to self-protect themselves against adverse effects of structural irregularities and other defects. Avoiding such structural irregularities in the material makeup would require a high energetic cost (e.g., through the need for strong bonding as it appears in crystalline solids). Biological materials appear to solve this challenge by adapting a structure that is intrinsically capable of mitigating structural irregularities or flaws while maintaining high performance, presenting a built-in capability to tolerate defects. These properties effectively result in self-protecting and flaw-tolerant materials.

The ability of the material to change its structural makeup, as demonstrated here by changing the crack orientation, reflects a level of responsiveness that transcends the concept of “static” structural optimization of hierarchical structures as described in the previous section. It mirrors an innate ability of biological materials to adapt to the environment by mutating their structural makeup at multiple scales and as such demonstrates that cross-scale interactions are crucial elements in understanding the mechanical performance of these materials.

Adaptive material properties

The adaptability of biological materials goes far beyond intrinsic mechanisms of crack shape change or flaw-tolerance that are built-in biological materials and structures. A greater level of adaptability can also involve cascades of signaling that link mechanical or other material cues to biochemical signals, resulting in the alteration of structure or the formation of new tissue. In this section we provide a brief review of how an important biological process, angiogenesis (the process of new blood vessel formation from existing vessels) respond and adapt to environmental cues via signaling cascades. The mechanism that regulates angiogenesis is complex and has been demonstrated to occur through the coupling of mechanical strain signals to biochemical factors, where the secretion of endogenous angiogenic factors was shown to be regulated by strain at multiple scales (Yung et al., 2009a). This example illustrates how biological systems are capable of adapting to different boundary conditions by forming new tissue via the coupling of material synthesis and structure formation with physiological cues. The significance of this aspect of protein materials in the context of the focus of this paper is that it shows that the study of biological systems with material concepts alone is insufficient. Rather, biological materials must be understood as complex hierarchical signaling cascades that are interrelated and that involve intervention mechanisms that are rooted in changing the structure of the most fundamental constituents, through altering gene expression.

Angiogenesis requires an orchestrated series of cell activities in a specific spatial and temporal sequence. Figure Figure66 summarizes the key results and a potential mechanobiological mechanism of angiogenesis. These nascent vessels feature a characteristic bilayer makeup of endothelial cells, which serve as the blood barrier, and surrounded by a supportive elastic layer of smooth muscle cells. Human umbilical vein endothelial cells (HUVECs) and human aortic smooth muscle cells (HASMCs) were used in these studies as model cell types to study the angiogenic process. A schematic illustration of a microdevice used to apply cyclic strain at 1 Hz to the cell cultures, cultured in PDMS wells, is shown in Fig. Fig.6A6A (Yung et al., 2009b). The application of mechanical strain was used to replicate the physiologic environment, where endothelial and smooth muscle cells are exposed to cyclical pulsations due to change in hemostatic pressures. A model system used to examine sprouting, a process identified to represent angiogenesis, is shown in Fig. Fig.6B6B where confocal images show HUVECs seeded onto microcarriers, embedded into fibrin gels, and forming tubelike extensions in response to specific cues. HUVECs cultured under static (no strain) conditions as shown in the left, form minimal sprouts, whereas those subject to cyclic strain, image to the right, form an enhanced quantity of sprouts. These images qualitatively demonstrate how cyclic strain significantly enhances sprout formation, suggesting that mechanical cues alone are capable of triggering the formation of nascent blood vessels. The mechanism that regulates this angiogenic process, here represented by sprout formations, is analyzed through examination of angiogenic biochemical factors regulated by strain. Figure Figure6C6C displays the temporal pattern of angiogenic factors secreted by HUVECs (PDGF and Ang-2) and HSMCs (VEGF and Ang-1) in response to cyclic strain. The results show that Ang-2 and PDGF are both upregulated in a temporal fashion relevant to their role in the angiogenic process, where the Ang-2 peak secretion occurred approximately at day 1 and the PDGF peak at day 2.

Figure 6
Examining the mechanobiological mechanism of angiogenesis (Yung et al., 2009a).

A potential mechanism of angiogenesis, as regulated by cyclic strain, is shown in Fig. Fig.6D6D demonstrating a coupled mechanical-biochemical process. The availability of Ang-2, an early angiogenic factor, in the microenvironment (via upregulated secretion in response to strain) resulted in the increased formation of HUVEC sprouts. Whereas the offset increased secretion of PDGF, a late stage cytokine, and chemotactant for HASMCs resulted in the recruitment of HASMCs, are likely to stabilize the nascent blood vessels (sprouts) in order to form the characteristic bilayer geometry of HUVECs and HASMCs. Under a lack of cyclic strain, both the Ang-2 secretion and PDGF secretion are reduced, resulting in reduced angiogenic activity. The mechanistic role of Ang-2 in strain regulated angiogenesis was examined using molecular biology knockdown techniques (RNAi), where the endogenous production of Ang-2 was suppressed. The angiogenic activity was reduced, both under static and more clearly, under stained conditions, thus verifying Ang-2’s causal role in strain regulated angiogenic activation. The study reviewed here showed that autocrine signaling via activation of Ang-2 may be the mechanistic pathway by which HUVECs transduce mechanical signals to process angiogenic responses. Furthermore, cyclic strain modulated the intercellular communication between endothelial cells and smooth muscle cells by upregulating chemotactic paracrine factors secreted by HUVECs to recruit HASMCs. The study reviewed in Fig. Fig.66 shows for the first time, that a single mechanical input can regulate intercellular biochemical communication between vascular cells to activate angiogenesis.

Universality-diversity paradigm of biological protein materials

The evolution of protein materials through genetic selection and structural alterations has resulted in a specific set of protein building blocks that define their structural makeup. As outlined throughout this article, protein materials exist in an abundant variety and the need exists to formulate a widely applicable model to systematically categorize all such materials in order to establish a fundamental understanding and to exploit the use of hierarchical structural building blocks to develop a new generation of advanced nanomaterials (Csete and Doyle, 2002; Alon, 2007; Buehler and Yung, 2009). A protocol is defined here as a term that encompasses a general analysis of protein materials that describes the use of structural building blocks (e.g., alpha-helices, beta-sheets, and random coils) during their formation and function, and the process or mechanism of use of this material (e.g., synthesis, breakdown, and self-assembly). The phenomenon of universality exists ubiquitously in biology, where certain protocols are commonly found in all protein materials (such as the use of hierarchical levels of building blocks: DNA nucleotides, DNA double helical structure, alpha-helices, and beta-sheets) and the process of transcription/translation, protein synthesis etc.). However, other protocols are highly specialized (such as the use of specific DNA sequences for a particular protein structure, the resultant protein motifs of tendon fascicles, lattice-like lamin structure, etc.), thus representing diversity. Therefore, protocols can be classified as either universal or diverse.

Universal and diverse protocols are distributed heterogeneously across different hierarchical levels, as shown in Fig. Fig.7.7. The four DNA nucleotides (ACGT) represent a universal protocol common to all protein materials, where their arrangements in diverse patterns form the immense variety of genetic sequences found in biology. Genetic sequences are universally encoded in the double-helical DNA structure, regardless of the specific nucleotide sequence. Through the universal process of transcription and translation, protein molecules are synthesized into a one-dimensional sequence of the universal 20 amino acid building blocks, which fold into 3D protein structures. Virtually all protein structures contain one or more of the universally found motifs: alpha-helices, beta-sheets, and random coils. These universal motifs arrange into unique, diverse larger-scale protein structures (e.g., enzymes, fibers, and filaments). Generally, a greater diversity of protocols is found at higher hierarchical levels, suggesting that biological functionality is associated with structural diversity. Universality is generally associated with protocols that can be used to derive diverse functionality at larger hierarchical levels. A fundamental difference between engineered materials and naturally formed biological materials is that functionality in biology can be created by arranging universal building blocks in different patterns, rather than by inventing new types of building blocks, as in many engineered materials. The formation of hierarchical arrangements provides the structural basis to enable the existence of universality and diversity within a single material. This combination of dissimilar concepts may explain how protein materials are capable of combining disparate material properties such as high strength and high robustness together with multifunctionality.

Figure 7
Universality and diversity of the structural makeup of biological protein materials, as discussed in Buehler and Yung (2009).

Biological functionality must be understood at varying scales. Biochemistry focuses on biological functionality at the molecular scales. The mesoscale that encompasses length-scales that range from nanometers to micrometers and time-scales of nanoseconds to microseconds is a particularly important level necessary to understand how specific protein materials derive their unique properties and what role they play in biological systems. Many material properties and mechanisms associated with physiologic and pathologic phenomena originate at this scale. The mesoscale science of protein materials, through the linking of molecular properties to properties of protein materials at the microscale, thus represents an important frontier of materials science with high potential for fundamental contributions to biology, medicine as well as for the de novo synthesis of engineered materials such as polymer nanocomposites and other hierarchical materials derived from self-assembly mechanisms (Glotzer and Solomon, 2007).

The approach of utilizing universal building blocks to create diverse multifunctional hierarchical structures has been successfully applied in current macroscale engineering paradigms. For example, in the design of structures such as buildings or bridges, universal constituents (bricks, cement, steel trusses, and glass) are combined to create multifunctionality (structural support, living space, thermal properties, and light harvesting) at larger length-scales. The challenge of utilizing similar concepts that span to the nanoscale, as exemplified in biological protein materials, through the integration of structure and material, could enable the emergence of novel technological concepts. A key obstacle in the development of new materials lies in our inability to directly control the structure formation at multiple hierarchical levels, an area of research that should be actively pursued from both an experimental and theoretical angle. The concept of universality and diversity and the knowledge gained from how to characterize these materials at different hierarchical levels can hopefully contribute to addressing these challenges.

As discussed in Buehler and Yung (2009), nature’s utilization of a limited number of universal building blocks, arranged diversely in a variety of ways, is a limitation as well as a strength of biological systems that could be exploited for materials design. For example, although the performance of structural tissues in our body is poor compared with most engineered materials (e.g., steel, ceramics, and composites), their performance is remarkably good considering the inferior building blocks they are made out of. Understanding these material concepts and the translation to the design of synthetic materials, perhaps based on new nanostructured building blocks such as carbon nanotubes or graphene platelets, could thus provide us with new ideas for materials design based on inexpensive, abundant constituents.


Biology utilizes hierarchical structures in an intriguing way to create multifunctional materials. This explains the formation of hierarchical structures with defined length-scales for key protein domains that are, as a consequence, found as universal features. We have further observed that the cascaded activation of deformation mechanisms at multiple scales enables the material to tolerate structural flaws (cracks) of virtually any size, representing an innate mechanism of structural transformation that enables protein materials to mutate their structure to cope with the adverse effects of a structural flaw. Complex biological feedback loops explain additional mechanisms of adaptation of biological to changes in the environment or to deal with new physiological requests (such as blood vessel formation). As shown in the example discussed here, mechanical strain signals at the scale of 10–100 cells (≈2000 μm) induce the secretion of signaling proteins at the molecular level (≈10–100 Å). Diffusive processes in the tissue transport these signaling proteins that activate cell-cell interactions at the level of several cells (≈100 μm). This example shows a complex interplay of biochemistry, mechanics, and material properties. Table Table33 summarizes the key mechanisms by which protein materials balance strength, robustness and adaptability.

Table 3
How protein materials balance strength, robustness and adaptability.

Materiomics is a powerful approach to investigate biological systems from this perspective (Buehler and Keten 2008; Buehler et al., 2008). Figure Figure8A8A shows the conventional materials science triangle that links structure, process and property. Figure Figure8B8B displays the materials science paradigm applied to the hierarchical structure of protein materials (Hi refers to hierarchy levels i=0…N, and Ri refers to material property requirements at hierarchy levels i=0…N). The expanded triangle shown in Fig. Fig.8B8B specifically includes the link of material properties and genetic processes (such as gene activation), which play a key role in understanding adaptability of biological materials. Thereby, biochemical processes facilitated by sensing of the environment of cells (as illustrated here for the example of angiogenesis) may change gene expression or activation, which results in inducing a change in cell behavior. This type of research, understanding the role of materials at the interface of physics, chemistry, and biology, could have great impact in various areas of biological and biomedical research. For example, atherosclerosis (hardening of blood vessels due to plaque formation) or blood clots in large vessels (e.g., carotid artery) and other blood vessel diseased states are related to a complex interplay of materials-cell interactions at multiple scales.

Figure 8
Conventional materials science paradigm (panel A) and hierarchical materials science paradigm applied to biological systems, referred to as materiomics (panel B).

The ability to adapt to changes in the environment and to provide simultaneously strength and robustness is a behavior that is in stark contrast to engineered materials (e.g., metals or ceramics; materials constructed with no hierarchies), where the presence of cracks leads to a severe reduction in strength and is the most common cause for catastrophic materials failure (Broberg, 1990). Materials failure typically initiates at locations of peak internal material stress at the corners of cracks), where atomic bonds are likely to break, leading to the propagation of fractures. Unfortunately, flaws and cracks in materials cannot be avoided. The current engineering paradigm to address this issue is to over-dimension materials, which has resulted in heavyweight structures where most of the excess material is never needed during regular operation. Biological materials, however, have an intrinsic ability to mitigate the adverse effects of material flaws (cracks) and are capable to render them innocuous, even to very large cracks. It was demonstrated (Ackbarow et al., 2009c) that the hierarchical makeup facilitated the dissipation of the local stress in the material by reorientating a crack in an alpha-helical protein network under tension from a horizontal to a vertical orientation, leading to a marginal increase in the stresses at the corners of the crack (Fig. (Fig.5).5). This change in the crack orientation provides a mechanism for the flawed material to deform several hundred per cent and still avoid catastrophic failure, despite the presence of large flaws. New computational strategies must be developed that are capable of incorporating changes at the genetic level into structural alterations at the level of proteins and protein assemblies. Such approaches could combine protein structure prediction methods with an analysis of the material performance and reveal interesting insight into the details of structure-process-property relationships.

For a variety of applications, cross-scale multiscale effects will be very important as we push the limits of what we can see and how small and how effective we can design, for example in the development of new types of composites that could be inspired from the structural features found in bone or nacre that could utilize fundamental scaling laws for strength and plasticity (Gao et al., 2003; Gao, 2006; Katz et al., 2007). For efficiency and conservation of finite resources, novel multiscale modeling methods will be required that enable us to explore the full design space, from nano to macro in a realization of a merger of structure and material. New interatomic force fields and potentials that can accurately describe the formation and breaking of diverse types of chemical bonds (H-bonds, covalent bonds, different solvent environments, etc.) in a seamless multiscale scheme are needed to include the full complexity of chemical bonding in a numerically efficient description. New types of models and approaches that bridge the knowledge between disparate engineering and scientific disciplines are necessary and may lead to emerging fields with huge potential impact for society and technological advancement as synergies between research fields are identified. The concept of designing materials with hierarchical structures, by deliberately determining a cascade of multiscale mechanisms is a largely unexplored aspect in materials science that could lead to advances in de novo materials design. By utilizing self-assembly processes from nano to macro (Reches and Gazit, 2007), hierarchical structures may be the key that can enable us to take advantage of properties at all scales, and to exploit superior nanoscale properties. Such work has the potential to extend the current state of the art toward developing a new generation of intelligent biomaterials that integrates structure and function, from the nano- to macroscales.


This research was supported by the Army Research Office (Grant No. W911NF-06-1-0291), the National Science Foundation (CAREER Grant Nos. CMMI-0642545 and MRSEC DMR-0819762), the Air Force Office of Scientific Research (Grant No. FA9550-08-1-0321), the Office of Naval Research (Grant No. N00014-08-1-00844), and the Defense Advanced Research Projects Agency (DARPA, Grant No. HR0011-08-1-0067). M.J.B. acknowledges support through the Esther and Harold E. Edgerton Career Development Professorship.


  • Ackbarow T, and Buehler M J (2007). “Superelasticity, energy dissipation and strain hardening of vimentin coiled-coil intermediate filaments: atomistic and continuum studies.” J. Mater. Sci. 42(21), 8771–8787.10.1007/s10853-007-1719-2 [Cross Ref]
  • Ackbarow T, and Buehler M J (2009a). “Alpha-helical protein domains unify strength and robustness through hierarchical nanostructures.” Nanotechnology 20, 075103.10.1088/0957-4484/20/7/075103 [PubMed] [Cross Ref]
  • Ackbarow T, Chen X, Keten S, and Buehler M J (2007). “Hierarchies, multiple energy barriers and robustness govern the fracture mechanics of alpha-helical and beta-sheet protein domains.” Proc. Natl. Acad. Sci. U.S.A. 104, 16410–16415.10.1073/pnas.0705759104 [PubMed] [Cross Ref]
  • Ackbarow T, Keten S, and Buehler M J (2009b). “Multi-time scale strength model of alpha-helical protein domains.” J. Phys.: Condens. Matter 21, 035111.10.1088/0953-8984/21/3/035111 [PubMed] [Cross Ref]
  • Ackbarow T, Sen D, Thaulow C, and Buehler M J (2009c). “Alpha-helical protein networks are self protective and flaw tolerant.” PLoS ONE 4(6), e6015.10.1371/journal.pone.0006015 [PMC free article] [PubMed] [Cross Ref]
  • Alberts B, Johnson A, Lewis J, Raff M, Roberts K, and Walter P (2002). Molecular Biology of the Cell, Taylor & Francis, New York.
  • Alon U (2007). “Simplicity in biology.” Nature (London) 446(7135), 497.10.1038/446497a [PubMed] [Cross Ref]
  • Arzt E, Gorb S, and Spolenak R (2003). “From micro to nano contacts in biological attachment devices.” Proc. Natl. Acad. Sci. U.S.A. 100, 10603–10606.10.1073/pnas.1534701100 [PubMed] [Cross Ref]
  • Autumn K, Sitti M, Liang Y A, Peattie A M, Hansen W R, Sponberg S, Kenny T W, Fearing R, Israelachvili J N, Full R J (2002). “Evidence for van der Waals adhesion in gecko setae.” Proc. Natl. Acad. Sci. U.S.A. 99, 12252–12256.10.1073/pnas.192252799 [PubMed] [Cross Ref]
  • Broberg K B (1990). Cracks and Fracture, Academic, London.
  • Buehler M J, and Ackbarow T (2007). “Fracture mechanics of protein materials.” Mater. Today 10(9), 46–58.10.1016/S1369-7021(07)70208-0 [Cross Ref]
  • Buehler M J, and Keten S (2008). “Elasticity, strength and resilience: a comparative study on mechanical signatures of α-helix, β-sheet and tropocollagen domains.” Nano Res. 1(1), 63–71.10.1007/s12274-008-8006-7 [Cross Ref]
  • Buehler M J, Keten S, and Ackbarow T (2008). “Theoretical and computational hierarchical nanomechanics of protein materials: deformation and fracture.” Prog. Mater. Sci. 53, 1101–1241.10.1016/j.pmatsci.2008.06.002 [Cross Ref]
  • Buehler M J, and Yung Y C (2009). “Deformation and failure of protein materials in physiologically extreme conditions and disease.” Nature Mater. 8(3), 175–188.10.1038/nmat2387 [PubMed] [Cross Ref]
  • Courtney T H (1990). Mechanical Behavior of Materials, McGraw-Hill, New York.
  • Csete M E, and Doyle J C (2002). “Reverse engineering of biological complexity.” Science 295(5560), 1664–1669.10.1126/science.1069981 [PubMed] [Cross Ref]
  • Dahl K N, Kahn S M, Wilson K L, and Discher D E (2004). “The nuclear envelope lamina network has elasticity and a compressibility limit suggestive of a molecular shock absorber.” J. Cell Sci. 117(20), 4779–4786.10.1242/jcs.01357 [PubMed] [Cross Ref]
  • Dahl K N, Ribeiro A JS, and Lammerding J (2008). “Nuclear shape, mechanics, and mechanotransduction.” Circ. Res. 102(11), 1307–1318.10.1161/CIRCRESAHA.108.173989 [PMC free article] [PubMed] [Cross Ref]
  • Dahl K N, Scaffidi P, Islam M F, Yodh A G, Wilson K L, and Misteli T (2006). “Distinct structural and mechanical properties of the nuclear lamina in Hutchinson–Gilford progeria syndrome.” Proc. Natl. Acad. Sci. U.S.A. 103(27), 10271–10276.10.1073/pnas.0601058103 [PubMed] [Cross Ref]
  • Folkman J (2003). “Fundamental concepts of the angiogenic process.” Current Molecular Medicine 3(7), 643–51.10.2174/1566524033479465 [PubMed] [Cross Ref]
  • Fratzl P (2008). Collagen: Structure and Mechanics, Springer, New York.
  • Fratzl P, and Weinkamer R (2007). “Nature's hierarchical materials.” Prog. Mater. Sci. 52, 1263–1334.10.1016/j.pmatsci.2007.06.001 [Cross Ref]
  • Fudge D, Russell D, Beriault D, Moore M, Lane E, and Vogl A (2008). “The intermediate filament network in cultured human keratinocytes is remarkably extensible and resilient.” PLoS ONE 3(6), e2327.10.1371/journal.pone.0002327 [PMC free article] [PubMed] [Cross Ref]
  • Gao H, Ji B, Jäger I L, Arzt E, and Fratzl P (2003). “Materials become insensitive to flaws at nanoscale: lessons from nature.” Proc. Natl. Acad. Sci. U.S.A. 100(10), 5597–5600.10.1073/pnas.0631609100 [PubMed] [Cross Ref]
  • Gao H, Wang X, Yao H, Gorb S, and Arzt E (2005). “Mechanics of hierarchical adhesion structures of geckos.” Mech. Mater. 37(2–3), 275–285.10.1016/j.mechmat.2004.03.008 [Cross Ref]
  • Gao H J (2006). “Application of fracture mechanics concepts to hierarchical biomechanics of bone and bone-like materials.” Int. J. Fract. 138(1–4), 101–137.10.1007/s10704-006-7156-4 [Cross Ref]
  • Glotzer S C, and Solomon M J (2007). “Anisotropy of building blocks and their assembly into complex structures.” Nature Mater. 6(8), 557–562.10.1038/nmat1949 [PubMed] [Cross Ref]
  • Houben F, Ramaekers F C, Snoeckx L H, and Broers J L (2007). “Role of nuclear lamina-cytoskeleton interactions in the maintenance of cellular strength.” Biochim. Biophys. Acta 1773(5), 675–86.10.1016/j.bbamcr.2006.09.018 [PubMed] [Cross Ref]
  • Janmey P A, Euteneuer U, Traub P, and Schliwa M (1991). “Viscoelastic properties of vimentin compared with other filamentous biopolymer networks.” J. Cell Biol. 113(1), 155–160.10.1083/jcb.113.1.155 [PMC free article] [PubMed] [Cross Ref]
  • Kageshima M, Lantz M A, Jarvis S P, Tokumoto H, Takeda S, Ptak A, Nakamura C, and Miyake J (2001). “Insight into conformational changes of a single alpha-helix peptide molecule through stiffness measurements.” Chem. Phys. Lett. 343(1–2), 77–82.10.1016/S0009-2614(01)00678-9 [Cross Ref]
  • Katz J L, Misra A, Spencer P, Wang Y, Bumrerraj S, Nomura T, Eppell S J, Tabib-Azar M (2007). “Multiscale mechanics of hierarchical structure/property relationships in calcified tissues and tissue/material interfaces.” Mater. Sci. Eng., A 27(3), 450–468.10.1016/j.msec.2006.05.055 [PMC free article] [PubMed] [Cross Ref]
  • Keten S, and Buehler M J (2008a). “Geometric confinement governs the rupture strength of h-bond assemblies at a critical length scale.” Nano Lett. 8(2), 743–748.10.1021/nl0731670 [PubMed] [Cross Ref]
  • Keten S, and Buehler M J (2008b). “Strength limit of entropic elasticity in beta-sheet protein domains.” Phys. Rev. E 78, 061913.10.1103/PhysRevE.78.061913 [PubMed] [Cross Ref]
  • Kreplak L, Herrmann H, and Aebi U (2008). “Tensile properties of single desmin intermediate filaments.” Biophys. J. 94(7), 2790–2799.10.1529/biophysj.107.119826 [PubMed] [Cross Ref]
  • Lammerding J, Schulze P C, Takahashi T, Kozlov S, Sullivan T, Kamm R D, Stewart C L, and Lee R T (2004). “Lamin A/C deficiency causes defective nuclear mechanics and mechanotransduction.” J. Clin. Invest. 113(3), 370–378. [PMC free article] [PubMed]
  • Lantz M A, Jarvis S P, Tokumoto H, Martynski T, Kusumi T, Nakamura C, and Miyake J (1999). “Stretching the alpha-helix: a direct measure of the hydrogen-bond energy of a single-peptide molecule.” Chem. Phys. Lett. 315(1–2), 61–68.10.1016/S0009-2614(99)01201-4 [Cross Ref]
  • Lawn B R (1993). Fracture of Brittle Solids, Cambridge University Press, Cambridge, U.K.
  • LeDuc P, and Schwartz R (2007). “Computational models of molecular self-organization in cellular environments.” Cell Biochem. Biophys. 48(1), 16–31.10.1007/s12013-007-0012-y [PubMed] [Cross Ref]
  • Meyers M A, Chen P Y, Lin A YM, and Seki Y (2008). “Biological materials: structure and mechanical properties.” Prog. Mater. Sci. 53(1), 1–206.10.1016/j.pmatsci.2007.05.002 [Cross Ref]
  • Qin Z, Cranford S, Ackbarow T, and Buehler M J (2009a). “Robustness-strength performance of hierarchical alpha-helical protein filaments.” Int. J. Appl. Mech. 1(1), 85–112.10.1142/S1758825109000058 [Cross Ref]
  • Qin Z, Kreplak L, and Buehler M J (2009b). “Hierarchical structure controls nanomechanical properties of vimentin intermediate filaments.” PLoS ONE 4(10), e7294.10.1371/journal.pone.0007294 [PMC free article] [PubMed] [Cross Ref]
  • Rammensee S, Slotta U, Scheibel T, and Bausch A R (2008). “Assembly mechanism of recombinant spider silk proteins.” Proc. Natl. Acad. Sci. U.S.A. 105(18), 6590–6595.10.1073/pnas.0709246105 [PubMed] [Cross Ref]
  • Reches M, and Gazit E (2007). “Peptide nanomaterials: self-assembling peptides as building blocks for novel materials.” In Nanomaterials Chemistry: Novel Aspects and New Directions, Rao C NR, Mueller A, and Cheetham A K (eds) pp 171–183, Wiley-VCH, Weinheim.
  • Sivaramakrishnan S, DeGiulio J V, Lorand L, Goldman R D, and Ridge K M (2008). “Micromechanical properties of keratin intermediate filament networks.” Proc. Natl. Acad. Sci. U.S.A. 105, 889–894.10.1073/pnas.0710728105 [PubMed] [Cross Ref]
  • Sullivan T, Escalante-Alcalde D, Bhatt H, Anver M, Bhat N, Nagashima K, Stewart C L, and Burke B (1999). “Loss of A-type lamin expression compromises nuclear envelope integrity leading to muscular dystrophy.” J. Cell Biol. 147(5), 913–919.10.1083/jcb.147.5.913 [PMC free article] [PubMed] [Cross Ref]
  • Vollrath F, and Porter D (2006). “Spider silk as archetypal protein elastomer.” Soft Matter 2(5), 377–385.10.1039/b600098n [Cross Ref]
  • Weitz D A, and Janmey P A (2008). “The soft framework of the cellular machine.” Proc. Natl. Acad. Sci. U.S.A. 105, 1105–1106.10.1073/pnas.0711639105 [PubMed] [Cross Ref]
  • Yung Y C, Chae J, Buehler M J, Hunter C, and Mooney D (2009a). “Cyclic tensile strain triggers a sequence of autocrine and paracrine signaling to regulate angiogenic sprouting in human vascular cells.” Proc. Natl. Acad. Sci. U.S.A. , 106(36), 15279–15285.10.1073/pnas.0905891106 [PubMed] [Cross Ref]
  • Yung Y C, Vandenburgh H, and Mooney D J (2009b). “Cellular strain assessment tool (CSAT): precision-controlled cyclic uniaxial tensile loading.” J. Biomech. 42(2), 178–82.10.1016/j.jbiomech.2008.10.038 [PubMed] [Cross Ref]

Articles from HFSP Journal are provided here courtesy of HFSP Publishing.