Integrated multiscale biomaterials experiment and modelling: a perspective

Abstract

Advances in multiscale models and computational power have enabled a broad toolset to predict how molecules, cells, tissues and organs behave and develop. A key theme in biological systems is the emergence of macroscale behaviour from collective behaviours across a range of length and timescales, and a key element of these models is therefore hierarchical simulation. However, this predictive capacity has far outstripped our ability to validate predictions experimentally, particularly when multiple hierarchical levels are involved. The state of the art represents careful integration of multiscale experiment and modelling, and yields not only validation, but also insights into deformation and relaxation mechanisms across scales. We present here a sampling of key results that highlight both challenges and opportunities for integrated multiscale experiment and modelling in biological systems.

1. Introduction

Biomaterials present a stunning diversity of forms built from a very few universal building blocks. In nearly all biomaterials, macroscale structure emerges over a series of hierarchies, and macroscale response derives from the temporal responses of these hierarchies. Tools established to predict macroscale material behaviour from first principles are now being harnessed to design and understand a broad range of biomaterials [1,2], and the range of tools for imaging the responses of these materials is growing steadily [3].

Central to the development of many of our modern predictive tools for the structure and behaviour of hierarchical biomaterials is the universality–diversity paradigm: highly conserved motifs emerge at each level hierarchy, motivating coarse-grained approximations that allow the simple passing of information from one hierarchy to the next [4–6]. This paradigm enables the simple application of tools such as those of category theory to understand biomaterials and tailor man-made biomimetic materials. In this light, the construction of a biomaterial from basic building blocks has been compared with the construction of a symphony from basic pressure waves (figure 1). In the same way that simple pressure waves, repeated and combined in specific patterns, can be combined to develop a symphony, simple proteins, repeated and combined in specific patterns, can be combined to form a complicated structure such as a spider web. The analogy also extends to simulation: music synthesizer software can simulate how these basic building blocks combine to form a symphony, and multiscale tools can simulate the mechanical response of a spider web from atoms to superstructure. The analogy is sufficiently robust that a musical arrangement was published recently whose composition could be attributed in part to a spider [5,7].

Figure 1.

The universality–diversity paradigm describes how complex biological materials systems such as spider webs can arise from structured combination and repetition of a small number of units, much in the same way that a symphony arises from structured combination and repetition of pressure waves. However, unlike the instruments and instrumental parts comprising a symphony, the hierarchical components comprising a biological material often cannot be tested and validated independently. Figure reprinted with permission from Buehler [4]. (Online version in colour.)

However, the analogy does not extend to model validation. The director of an orchestra can examine both the score and the performers at any level of hierarchy. Each individual part can be examined solo, and the tone and tuning of each instrument can be examined. For multiscale measurement and simulation of biomaterials, many phenomena cannot occur outside of the proper hierarchical context. As an example, cells from solid tissues examined outside of their three-dimensional context typically adopt entirely different morphologies, obscuring the validation of the biophysical models predicting cell behaviour.

Additionally, validation of multiscale models for biomaterials is hindered by the availability of tools to probe certain phenomena over critical spatio–temporal regimes even if the processes were accessible to observation. As an example, consider the validation of models for the formation of membrane rafts on living cells (cf. [8]). Nanoscale membrane rafts are believed to be important in a range of signalling events, but characterizing their dynamics and availability is complicated by their size range, which lies below the optical resolution limit. Models exist for lipid dynamics across the entire range of physiologically relevant hierarchies, from the nanometre and nanosecond length and timescales of rotational diffusion to the tens of micrometre and hundreds of second length and timescales of bulk diffusion (dark patches (red); figure 2). A range of at least partially applicable imaging technologies covers most of the range of biophysical phenomena that one would hope to validate (light, dashed patches (yellow); figure 2). These include neutron scattering techniques at the smallest length and timescales, and optical and fluorescence techniques at the longest length and timescales, with techniques such as atomic force microscopy in upper left corner corresponding to short length scales and long timescales. However, broad patches exist with no coverage by any imaging modality, and no single imaging modality covers the entire range of phenomena.

Figure 2.

A central challenge in verification of multiscale simulations is the absence of imaging modalities across certain length and timescale ranges. For the physical processes believed to underlie the dynamics of membrane raft formation (dark-coloured boxes, red), several regions exist in which no existing imaging modality can validate models (light-coloured dashed boxes, yellow). No single imaging modality spans the entire range of relevant length or timescales. Based upon figures presented in Elson et al. [8]. (Online version in colour.)

The result is a need for tight integration between experiment and simulation to be able to ‘spot check’ model predictions under conditions for which measurements are available, and to establish confidence intervals for predictions in conditions between these spot checks. The problem extends to nearly all aspects of biophysical and biomaterials modelling, and constitutes a major challenge for the field. The problem constitutes an important focus of the Interagency Modelling and Analysis Group (IMAG), a joint effort of 10 funding agencies from the USA and Canada, and is the central focus of the IMAG's ‘integrated multiscale biomaterials experiment and modelling’ working group that we chair.

This special issue of Interface Focus brings together contributions on this topic by leading experts, with the aims of establishing a snapshot of the state of the art and of identifying key challenges and opportunities. The contributions fall into four major categories: the mechanics of fibrous, hierarchical structural protein networks; the often recursive interactions of cells and extracellular matrix (ECM); the interactions between proteins and stiff mineral particles; and the study of human systems.

2. Mechanics of structural protein networks

A central motif in biological materials is the resistance of tensile loads by bundles of nanofibers arranged hierarchically. Although this has been recognized for decades, many important mysteries persist relating to understanding of the fibres themselves and of their mesoscale interactions. As reviewed by Fang & Lake [9], the field has gradually progressed from simple phenomenological models to intricate structural models that account for details of fibre response, architecture and interactions. This issue presents several major advances in this area, and highlights open challenges.

Collagen is the most abundant protein in the human body. One of the most fundamental barriers to modelling collagenous tissues has been the inability to directly match experiment and prediction for possibly the most important mammalian protein structures, collagen fibrils. This is not simply because of the mismatch between the timescales available to atomistic studies and those available to experiment: a single collagen fibril experiment had never been performed before the work presented by Liu et al. [10]. Additionally, the interactions between loaded collagen fibrils and fibres are difficult to model. A major modelling advance accounting for cross-linking between collagen fibres is presented by Sacks et al. [11], and a major step forward in our understanding of interactions between the many types of collagen within connective tissues is presented by Connizzo et al. [12]. However, balancing these substantial advances in understanding is a substantial advance in confusion put forth by Susilo et al. [13], who present a new and unprecedented finding that collagen is sensitive to the way in which it is loaded: although strain-dependent enzymatic digestion of collagen has been well documented, Susilo et al. [13] report for the first time, to the best of our knowledge, that cyclical loading fundamentally stiffens networks of collagen.

More generally, the mechanical properties of protein networks are affected by the formation and dissociation of bonds between fibres. Mobility of these cross-linking interactions at high load is a highly conserved mechanism for toughening of biomaterials. A new framework for predicting degradation of protein networks and the associated mechanical changes to a tissue is presented by Nims et al. [14]. This framework is based upon the tracking of a state variable related to bond dissociation statistics, and has the distinct advantage of tight integration with experiment through measurement of the state variable's evolution. Reconstituting mobile fibre–fibre interactions in vitro typically involves chemical cross-links between fibres. A novel approach replaces chemical bonds with knotted entanglement, and this is embodied for the first time in a silk fibre network by Berardo et al. [15].

3. Cell–extracellular matrix feedback

Cells adapt to and modify the ECM that surrounds them. The first example of this in the literature relates to the adaptation of bone to mechanical loading, following Wolff's law. Despite over a century of work on the subject, the basic mechanisms of mechanoresponsiveness and mechanoadaptations in bone are still unclear. As described by Brown et al. [16], a key challenge is validation of multiscale validation, with relevant timescales in bone remodelling ranging from milliseconds to weeks, and repellent length scales ranging from micrometres to metres. Nevertheless, several very promising advances have emerged in the past several years, and, as discussed by Brown et al. [16], coupled modelling and experiment offer much promise for unlocking the keys to bone mechanoadaption.

Unlocking the rules that cells follow constitutes a crucial challenge for the design of synthetic tissues and for understanding and combatting a range of mechanobiological pathologies. One of the most important tools for this is tissue constructs that present simplified systems in which to probe the biophysical responses of cells to mechanical and biochemical stimuli including drugs [17]. The function of tissue constructs as both testbeds for basic science and platforms for drug discovery centre on tight integration of experiment, biochemical treatment and multiscale modelling, as reviewed by Elson & Genin [17].

Two recent breakthroughs in the analysis of cells in collagenous environments are presented. In the first, Gyoneva et al. [18] present a groundbreaking model of how cells compress and remodel collagen through strain-dependent degradation of collagen fibres and rule-based synthesis of new collagen. A key open question is how to break through the challenge of validation at the mesoscale: the remodelling outcomes observed were exquisitely sensitive to the rules chosen for remodelling, and imaging to compare rules poses a spatiotemporal imaging challenge. In a second, related breakthrough, Shenoy et al. [19] present a model of stress-dependent recruitment of myosin motors, which is central to the form and function of a broad range of living cells, and is a highly sensitive to the mechanical environment of the pericellular region. The ability to model this and its effects on cell form and function has posed a long-standing challenge to the field, and the field has had a number of partially phenomenological solutions. Shenoy et al. [19] present a major advance in this effort by placing this field on a solid thermodynamic footing, a milestone for the field. As with the work of Gyoneva et al. [18], this latter work matches with a broad range of existing experimental observation, and points the way for interesting new validation experiments to be performed.

4. Mineral–collagen interactions

Interactions between collagen and mineral are central to the mechanics and resilience of bone [20,21] and its interfaces with soft tissues [22,23]. A range of phenomenological and mechanistic models exist for the strength and toughness of bone, as reviewed by Jasiuk et al. [24]. Reconstituting these in a tissue construct, especially a scaffold intended for functionally graded tissue attachment, is a challenge, because the details of protein–mineral interactions are still not known in bone and partially mineralized tissues. Two major factors are deriving models for interactions between proteins and charged surfaces, and identifying and modelling the structures that enable mineral–collagen interaction in bone. A substantial advance is presented by Martin et al. [25] in the former area, with a transformative new framework for this type of simulation. In the latter area, Smith et al. [26] present an integrated modelling and experimental study that seemingly argues against the hypotheses that mineral and collagen interact mechanically in a significant way in bone without the action of additional supporting protein structures. Much scope exists for integrated experiment and modelling to dissect the mechanisms of mineral–collagen interactions.

5. Human systems

A key challenge in modelling biological materials is that they arise from individuals who can differ tremendously. Planning of treatment, assessment of injury and mapping of anatomy all rely on robust integration of theory and experiment in a way that can be adapted to a specific individual. This adds a layer of complexity, but tools are becoming available to address this complexity. We present five papers that encapsulate the state of the art.

A spectrum of next-generation treatments aim to deliver drugs that are tailored to a patient directly to sites of pathology. The delivery of nanoparticulate chemotherapy agents to the site of a tumour currently relies on the leaky vasculature typically present at a tumour, but nanoparticles that preferentially bind to protein targets at a tumour site are currently in various stages of development. The ability to predict the microvasculature distribution and endocytosis of such particles will form an important tool to plan and optimize such treatments. Li et al. [27] present the state of their current efforts to produce such a treatment planning tool. In addition to drug delivery planning, Elson & Genin [17] describe a vision in which drug efficacy and cardiotoxicity can be tested through integrated modelling and experiment on tissue constructs derived from a patient's own cells.

An important part of patient-specific medicine is validation of the approaches and models used to design these treatments. Li et al. [28] describe an elegant technique for assessing how a specific patient's blood would respond to treatment for sickle-cell anaemia. Although the mesoscopic validation of these approaches is still developing, comparisons among multiscale modelling predictions for specific patients enable the development of guidelines for treatment and also enables the identification of optimal metrics for determining patient responses to treatment.

The next example of mapping human-specific complexity involves efforts to map the structure and function to the human brain. Although electron microscopy and magnetic resonance imaging have been dominant to date, a series of advanced fluorescence-based tools are becoming available that enable the rapid and accurate mapping of a specific animal's synaptic connections. As described by Hogstrom et al. [29], these tools, concert with mathematical tools to integrate electron and fluorescence microscopy datasets, promise unprecedented cross-validation of mappings and a foundation for multiscale, structure-based modelling of brain function.

The final example is one in which substantial uncertainty exist in both experiment and modelling. Current models of brain injury fail to capture the ways that repeated insult to the head relates to the likelihood of traumatic brain injury. Detailed computer models, eventuality to be based upon data like that described by Hogstrom et al. [29], can be used to make estimates of mechanical fields such as stress and strain within the brain, but these models are too slow to run on an entire football season's worth of accelerometer data from a single player. Zhao & Ji [30] describe the validation of brain atlas techniques to estimate pressure histories within the heads of individual athletes over very large datasets, and discuss challenges and opportunities ahead for such approaches as the field steps towards more biophysically based injury criteria.

6. Perspectives

A rich set of tools exists for validating multiscale models for hierarchical biomaterials through integration of modelling and experiment. A central challenge that emerges in nearly all of the articles in this issue is a need to design experiments around certain phenomena that cannot be observed independently. For example, returning to the analogy of a symphony, cells taken out of their preferred tissue environment often behave erratically or simply die, much like a viola player when asked to play solo outside of the context of an orchestra. A perennial challenge is capturing and validating phenomena that occur at a mesoscale too large for first principles modelling, and too small for standard continuum modelling; just as a seasoned director knows to check for French horns playing in the wrong key, a seasoned engineer knows to check for inadequately modelled mesoscale phenomena.

Several examples exist of multiscale models that guide and aid with the interpretation of important experiment. As Nims et al. [14] discuss, an effective multiscale model contains state variables whose evolution can be measured quantitatively, and whose character describes the nature of critical experiments to be performed. By tracking the appropriate state variables, experiments can identify salient material behaviour and inform both the design of new materials and the treatment of disease. New paradigms for integrating multiscale models with biomaterials experiment continue to develop. As these unfold, they hold the potential to bring with them a new era of first principles treatment strategies and tailor-designed biological materials.