Elsevier

Progress in Materials Science

Volume 53, Issue 8, November 2008, Pages 1101-1241
Progress in Materials Science

Theoretical and computational hierarchical nanomechanics of protein materials: Deformation and fracture

https://doi.org/10.1016/j.pmatsci.2008.06.002Get rights and content

Abstract

Proteins constitute the building blocks of biological materials such as tendon, bone, skin, spider silk or cells. An important trait of these materials is that they display highly characteristic hierarchical structures, across multiple scales, from nano to macro. Protein materials are intriguing examples of materials that balance multiple tasks, representing some of the most sustainable material solutions that integrate structure and function. Here we review progress in understanding the deformation and fracture mechanisms of hierarchical protein materials by using a materials science approach to develop structure-process-property relations, an effort defined as materiomics. Deformation processes begin with an erratic motion of individual atoms around flaws or defects that quickly evolve into formation of macroscopic fractures as chemical bonds rupture rapidly, eventually compromising the integrity of the structure or the biological system leading to failure. The combination of large-scale atomistic simulation, multi-scale modeling methods, theoretical analyses combined with experimental validation provides a powerful approach in studying deformation and failure phenomena in protein materials. Here we review studies focused on the molecular origin of deformation and fracture processes of three types of protein materials. The review includes studies of collagen – Nature’s super-glue; beta-sheet rich protein structures as found in spider silk – a natural fiber that can reach the strength of a steel cable; as well as intermediate filaments – a class of alpha-helix based structural proteins responsible for the mechanical integrity of eukaryotic cells. The article concludes with a discussion of the significance of universally found structural patterns such as the staggered collagen fibril architecture or the alpha-helical protein motif.

Introduction

Proteins constitute critical building blocks of life, forming biological materials such as hair, bone, skin, spider silk or cells, which play an important role in providing key mechanical functions in biological systems [1], [2], [3], [4], [5], [6], [7], [8], [9]. Failure of these materials due to flaws or extreme chemical or mechanical conditions can cause diseases and malfunctions in biological organisms. This occurs for instance in genetic disorders (e.g. rapid aging disease progeria, brittle bone disease asteogenesis imperfecta, Alport’s syndrome, etc.), disease due to foreign material buildup such as in Alzheimer’s disease, or during injuries and trauma. However, the fundamental deformation, fracture general failure mechanisms of biological protein materials remain largely unknown, partly due to a lack of understanding of how individual protein building blocks respond to mechanical load and how they participate in the function of the overall biological system at the mesoscale.

Such understanding is vital to advance models of diseases, the understanding of biological processes such as mechanotransduction, or and bioinspired the development of biomimetic materials. Recent progress provides us with insight into such mechanisms and clarifies for the first time how biology “works” at the ultimate, molecular scale, and how this relates to macroscopic phenomena such as cell mechanics or tissue behavior, across multiple hierarchical scales. This type of effort, the linking of mechanisms across multiple scales by using a materials science approach to provide structure-process-property links forms the emerging field of materiomics. This review article exemplifies theoretical and computational hierarchical nanomechanics approaches in the analysis of three representative protein structures, including collagenous tissues, beta-sheet rich protein materials and alpha-helix rich protein materials, illustrating how materiomics contributes to develop a de novo understanding of biological processes and to the potential of exploiting novel concepts in technological innovation.

The field of mechanical properties of hierarchical biological materials [1], [2], [3], [4], [5], [6], [7], [8] underwent an exciting development over the past several years, partly due to the emergence of physical science based approaches in the biological sciences, leading to cross-disciplinary investigations of materials, structures, diseases as well as the development of new treatment and diagnostics methods [10], [11], [12], [13].

Historically, commonly used materials have been instrumental in classifying stages of civilizations, starting with the Stone Age thousands of years ago and ranging to the so-called “silicon age” in the late 20th and early 21st century. Despite the extensive and very successful utilization of materials in addressing societal needs, a systematic analysis of materials in the context of linking chemical and physical concepts with engineering applications in a systematic paradigm to link structure, processes and properties and fundamental mechanisms has not been achieved until very recently.

For instance, 50 year ago, E. Orowan, M. Polanyi and G.I. Taylor have discovered dislocations, a concept proposed theoretically in 1905 by V. Volterra. It was discovered that dislocations represent the fundamental mechanism of plastic deformation of metals [14], [15]. Theoretical and physical understanding of dislocations and other nano- and microscopic deformation mechanisms was a prerequisite for major breakthroughs that utilized this knowledge for systematic material design. Advanced jet planes, cars, space shuttles and more recently, nanodevices, through synthesis of ultra-strong and heat resistant materials, could be a few examples of novel inventions that have benefited from discoveries regarding fundamental deformation mechanisms in metals. It is noted, however, that even without the knowledge of microscopic deformation mechanisms, the development of cars, airplanes and other technological achievements was possible.

Perhaps similar opportunities can be created today for the analysis and engineering of complex biological systems, based on quantitative insight into their fundamental physical and chemical features. A rigorous understanding may enable us eventually to integrate concepts from living systems into engineering materials design, seamlessly. Optical, mechanical and electrical properties at ultra-small material scales, their control, synthesis and analysis as well as their theoretical description represent major scientific and engineering opportunities. However, as in the case of conventional “engineered” materials, these breakthroughs may only be possible provided that their fundamental concepts are understood very well. Characterization of materials found in biology within a rigorous materials science approach is aimed towards the elucidation of these fundamental principles of assembly, deformation and fracture of these materials.

Deformation and fracture properties are intimately linked to the atomic microstructure of a material. Whereas crystalline materials show mechanisms such as dislocation spreading or crack extension, biological materials feature molecular unfolding or sliding, with a particular significance of rupture of chemical bonds such as hydrogen bonds, covalent cross-links or intermolecular entanglement. Fig. 1 displays an overview over the deformation and fracture behavior of different classes of materials, including ductile materials [15], brittle materials [16], as well as biological protein materials. Each subplot in Fig. 1 shows a multi-scale view of associated deformation mechanisms [17], [18]. Different mechanisms may operate at larger length- and time-scales, where the interaction with cells and of cells with one another, different tissue types and the influence of tissue remodeling become more evident. The dominance of specific mechanisms is controlled by geometrical parameters as well as the structural arrangement of the protein elementary building blocks, across many hierarchical scales, from nano to macro (Fig. 2).

It is known from other fields in materials science that nano- or microscopic structures and defects control the macroscopic material behavior: for example, grain size reduction or confinement leads to an increase of the strength of crystalline metals [19], [20], [21], [22]. Deformation maps have been proposed to characterize material properties for engineering applications [23]. Discovering similar insight for biological structures and materials represents a current frontier of research. A particularly challenging subject is the elucidation of the significance and role of nanostructures for macroscopic properties. Sensitivity analyses that show how small-scale features influence larger scale properties may effectively illustrate nanoscopic size effects in biological materials.

A major trait of biological materials is the occurrence of hierarchies and, at the molecular scale, the abundance of weak interatomic or intermolecular interactions (e.g. hydrogen bonds). The presence of hierarchies in biological materials may be vital to take advantage of molecular and sub-molecular features. For example, weak bonds in protein materials exist in hierarchical assemblies that work cooperatively to have a measurable influence for properties at larger scales. Although insignificant as individual bonds (in terms of their utilization as mechanical elements, e.g. as a glue), assemblies of weak non-covalent bonds governs structural organization and function [1], [2], [12], [24] of these materials. Utilization of weak interactions also makes it possible to produce materials at moderate temperatures and thus with limited energy use, as well with an intrinsic self-healing ability since such bonds can reform in situ. An important distinction between structural control in traditional and biological materials is the geometrical occurrence of defects. While defects are often distributed randomly over the volume in crystalline and other engineered materials, biological materials consist of an ordered structure that reaches down to the nano-scale. In many biological materials, defects are placed with atomistic or molecular precision, and may play a major role in the material behavior observed at larger scales. These features have been observed in bone, nacre, collagenous tissue or cellular protein networks, where some defects are highly conserved features that occur across multiple species.

Proteins are synthesized in biological systems based on sequence information encoded in the DNA (short for deoxyribonucleic acid). A series of DNA letter codes (nucleotides) is translated into the polypeptide sequence, which folds into complex three-dimensional geometries (for further details, please see [1]). This process is illustrated in schematically Fig. 3. A notable feature of this mechanism is the ability to control the structure of these materials at very small, atomistic scales, via the modification of the DNA sequence in the genetic code. Biological protein materials are typically formed by self-assembly processes, thereby forming complex hierarchical structures out of individual protein building blocks. The synthesis of a particular protein is directed via the activation of specific genes. This activation can be caused by biochemical or mechanical signals that lead to processes inside the cell’s nucleus.

The mechanical properties of biological protein materials have wide ranging implications for biology. In cells for instance, mechanical sensation is used to transmit signals from the environment to the cell nucleus in order to control tissue formation and regeneration [1], [25]. The structural integrity and shape of cells is controlled by the cell’s cytoskeleton, which resembles an interplay of complex protein structures and signaling cascades arranged in a hierarchical fashion. Bone and collagen, providing structure to our body, or spider silk, used for prey procurement, are examples of materials that have incredible elasticity, strength and robustness unmatched by many synthetic materials, which has been attributed to its structural formation with molecular precision [1], [8], [12], [4], [26], [27], [28], [29], [30], [31], [32], [33]. The translation of concepts observed in biology into technological applications and new materials design remains a big challenge. In particular, the combination of nanostructural and hierarchical features into materials developments could lead to significant breakthroughs.

What are the most promising strategies in order to analyze biological protein materials? Perhaps, an integrated approach that uses experiment and simulation concurrently could evolve into a new paradigm of materials research. Experimental techniques have gained unparalleled accuracy in both length- and time-scales (see Fig. 4), as reflected in development and utilization of Atomic Force Microscope (AFM) [34], [35], optical tweezers [10], [13], [29], [36] or nanoindentation [11], [12], [37], [38] to analyze biological materials. At the same time, modeling and simulation as well as theoretical approaches have evolved into predictive tools that complement experimental analyses (see Fig. 4).

In the field of atomistic-based multi-scale stimulation, it is now possible to begin from the smallest scales (considering electrons and atoms), to reach all the way up to macroscopic scales of entire tissues, by explicitly considering the characteristic structural features at each scale. Such approaches are possible with the advent of first principles based multi-scale simulation techniques (see, for instance a review article for a broad introduction into this field [39]). The basic principle underlying these multi-scale simulation methods is “finer scales train coarser scales”. Even though there are still major challenges ahead of us, the progress that has been reported thus far is encouraging and provides one with seemingly infinite possibilities, transforming materials science as a discipline through increased integration of computational approaches in scientific research.

A central theme of the efforts in developing materiomics is to appreciate the structure–property or structure–processing–property paradigm. This paradigm has guided materials science for many decades. For biological materials, there remain several challenges that make developing these rigorous links rather difficult and that cause for new analysis paradigms.

For example, bond energies in biological materials are often comparable to the thermal energy, as for instance in the case of hydrogen bonding, the most abundant chemical bond in biology. Biological materials often show highly viscoelastic behavior, since their response to mechanical deformation is intrinsically time-dependent. In many cases, biological structures contain extremely compliant filaments, in which entropic contributions to free energy are important and can even control the deformation behavior (e.g. elasticity and strength of hydrogen bonded protein domains [40]). Many material properties are further length scale dependent and can vary significantly. This poses grand challenges for the characterization of biological materials, as well as the comparison between different analysis approaches (e.g. simulation vs. experiment), since measuring different volumes of material lead to different material properties (e.g. elastic modulus, strength, as well as associated deformation mechanisms). Size dependent material properties are possibly crucial to understand the role of materials in physiological processes, and thus this area of research poses an exciting frontier of research. The presence of hierarchical structures calls for new paradigms in thinking about the structure–property paradigm, since corresponding concepts must include an explicit notion of the cross-scale and inter-scale interactions [40], [41].

It has become evident that the atomistic scale, and in particular the notion of a chemical bond, provides a very fundamental, universal platform of materiomics at which a variety of scientific disciplines can interact: chemists, through the molecular structure of proteins, physicists, through the statistical mechanics of a large number of atoms, and materials scientists through analysis of phenomena such as elasticity, optical properties, electrical properties or thermodynamics, linking structure and function. Fig. 5 illustrates this concept. A noteworthy aspect of the materials science of biological materials is that it is interdisciplinary, by nature. Performing research in this field thus often implies to overcome barriers between scientific disciplines and to develop strategies that enable us to communicate each other’s concepts more clearly. Structures in universities and research institutions may have to be modified to facilitate these new emerging frontiers of materials research.

It is vital to overcome the barrier that currently separates the understanding at different length- and time-scales, through the development of new experimental synthesis and characterization methods, novel model systems and an enhanced appreciation for a multi-scale view of materials in general, in order to fully understand multi-scale or cross-scale interactions in materiomics. To facilitate these developments, we must also develop a proper nomenclature to capture the various scales involved in a material. Current terminologies referring to atomistic, meso, micro and macro are insufficient to capture the subtleties of the various scales and structures observed in biological protein materials. Research should address the opportunities in integrating nanoscience and nanotechnology into biological research. What could our impact be, in the long-term perspective, in understanding some of the fundamental material concepts of biology?

For instance, is the nanomechanics of protein materials significant for biology, and may biologists have missed out on important effects due to a lack of consideration of the nanomechanics? Can we find inspiration from Nature that could guide us in the design of materials that are environmentally friendly, lightweight and yet tough and robust and can serve multiple objectives? How is robustness achieved in biology? How do universality and diversity of structural building blocks and mechanisms of material assembly or breakdown integrate into biological structures? From a theoretical viewpoint, major challenges include the development of new materials theories that include atomistic and statistical effects into an effective description, while retaining a system theoretical perspective of the overall material behavior [5], [32], [33], [40], [41], [42], [43]. This may eventually lead to a fruitful interaction between systems biology and materiomics.

Deformation mechanisms are a crucial element in understanding the response of materials to external stimuli. Similar to dislocation mechanics for metal plasticity, what is the theoretical framework for describing deformation and fracture of biological materials and elementary structures? It is possible that statistical theories may play a crucial role in the theoretical development of nanomechanics. Full-atomistic simulations of complex protein structures or large hierarchical protein assemblies with explicit solvents are often prohibitive due to computational limitations, and coarse-graining techniques must be used. In coarse-graining approaches, the full atomistic representation of protein structures is replaced by a model in which small groups of atoms are treated as individual (single) particles. Such methods represent a promising approach in analyzing key materials phenomena in biology focused on the mesoscale. Fig. 6 shows an example application of such a coarse-graining technique (see also Fig. 4, reference to “Mesoscale”). Fig. 6a and b shows coarse-graining approaches for membrane lipid molecule structures as reported in [44], where the left part shows the full atomistic representation and the right part the corresponding coarse-grained model. Fig. 6c shows the results of a coarse-grained simulation, showing the protein (red backbone trace) in the lipid bilayer at the end of the 200 ns simulation. Fig. 6d shows the backbone particle root mean square fluctuation (RMSF) as a function of residue number, for both the atomistic and the coarse-grained simulation, illustrating that the two descriptions provide similar results. Whereas coarse-graining works well for some systems, the method is not generally applicable and must typically be developed carefully for specific cases. Based on these challenges, it has been discussed how effective are coarse-graining techniques, overall? In general, can we indeed average out over atomistic or mesoscale structures to find equivalent representations for entire groups of atoms or are the atomistic details crucial for phenomena observed at larger length- and time-scales? How important are atomistic features at macroscale? What are the most appropriate numerical strategies to simulate the role of solvent (e.g. water) in very small confinement, where it can no longer be represented by continuum-type theories? How does confined water in small pores within and between protein constituents influence the mechanical response of natural and biological materials?

Progress in these various challenging fields will probably first occur specific to problems and applications, perhaps in those have most impact in medical or economic fields. Eventually, we must generalize our insight into the formulation of a holistic theoretical framework that transcends the current nomenclature, theoretical and experimental thinking. These efforts may provide the scientific and engineering fundamentals to develop and maintain the infrastructures to enable and evolve modern civilization. Through materiomics, materials – and materials science – could play a seminal role in these developments.

This review article provides an overview over advances in the field of deformation and fracture mechanics of biological protein materials, focusing on three model systems. The three model systems encompass the most abundant, universal building blocks of all protein materials: alpha-helices, beta-sheets and tropocollagen molecules. In each section, the article contains a broad review of works in this field. However, there is a particular focus on a summary of results reported by our group.

Section 2 provides an introduction into the numerical modeling techniques, in particular atomistic simulation methods. Section 3 provides a review of studies of collagenous tissues, including bone. Particular focus is on the mechanical properties and the properties of individual molecules and collagen fibrils. Section 4 is dedicated to a review of analyses of alpha-helical protein structures, focusing on vimentin intermediate filament protein structures. Section 5 is focused on the analysis of the mechanical properties of beta-sheet protein structures. The article concludes in Section 6 with a discussion and an outlook.

Section snippets

Atomistic and molecular modeling – introduction

Atomistic molecular dynamics (MD) is a tool for elucidating the atomistic mechanisms that control deformation and rupture of chemical bonds at nano-scale, and to relate this information to macroscopic material deformation and failure phenomena (see, e.g. references [18], [26], [27], [40], [44], [45], [46], [93], and recent articles from our group that describes large-scale MD simulation of brittle fracture mechanisms [47], [48], [49], [50], [51]). The basic concept behind atomistic simulation

Collagenous tissue

This section describes hierarchical multi-scale modeling of collagenous tissues, with a particular focus on the mechanical properties. Studies focus on elastic behavior, plastic behavior and fracture. Starting at the atomistic scale, we review the development and application of a hierarchical multi-scale model that is capable of describing the dynamical behavior of a large number of tropocollagen molecules, reaching length-scales of several micrometers and time-scales of tens of microseconds.

A

Alpha-helical proteins: intermediate filaments

The next protein structure considered is the class of alpha-helical (AH) proteins. Together with beta-sheets, AH structures are the most abundant secondary structures found in proteins. The AH motif is commonly found in many structural protein networks, forming the basis for biological protein materials such as hair, wool and the cell’s cytoskeleton. In particular, the AH protein motif plays an important role in biophysical cellular processes that involve mechanical signals, including

Beta-structured protein materials

This section focuses on beta-sheet and beta-helical secondary structures; key building blocks of muscle, viral, spider silk and amyloid fibers as well as many other biological materials with intriguing mechanical properties. We review computational and experimental results on the nanomechanics of protein structures that employ beta-sheets, illustrating the key link between this topological configuration and mechanically resistant protein domains found in biology. H-bond rupture mechanisms and

Discussion and conclusion

The review of results in the previous chapters has provided an overview over developments and capabilities of bottom-up computational models in studies of deformation and fracture of biological protein materials. In this final section we provide a discussion and an outlook to possible future research directions.

This review article was focused on three protein materials, collagenous tissues, alpha-helical rich protein materials, as well as beta-sheet rich protein materials. These represent some

Acknowledgements

This research was supported by the Army Research Office (ARO), Grant Number W911NF-06-1-0291 (program officer Dr. Bruce LaMattina), the Solomon Buchsbaum AT&T Research Fund, as well as a National Science Foundation CAREER Award (CMMI-0642545, program officer Dr. Jimmy Hsia). The authors acknowledge a supercomputing grant at the San Diego Supercomputing Center (SDSC). S.K. acknowledges support by the Presidential Graduate Fellowship Program at the Massachusetts Institute of Technology. In

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