Elsevier

Acta Biomaterialia

Volume 96, 15 September 2019, Pages 303-309
Acta Biomaterialia

Full length article
A microscopically motivated model for the swelling-induced drastic softening of hydrogen-bond dominated biopolymer networks

https://doi.org/10.1016/j.actbio.2019.07.005Get rights and content

Abstract

The penetration of water into rubber-like protein networks such as cross-linked resilin, which is found in insects, can lead to changes in stiffness that range over several orders of magnitude. This softening effect cannot be explained by the volumetric changes associated with pure swelling/deswelling used to describe networks with covalent bonds. Rather, this property stems from the reversible swelling-induced breaking of hydrogen cross-linking bonds that connect the chains in the network. This work presents a model for the swelling and the mechanical response of hydrogen-bond dominated biopolymer networks. It is shown that the penetration of water molecules into the network leads to the breaking of non-covalent cross-linking sites. In turn, the network experiences a reduction in the effective chain-density, an increase in entropy, and a consequent decrease in free energy, thus explaining the dramatic softening. Additionally, the breaking of hydrogen bonds alters the micro-structure and changes the quantitative elastic behavior of the network. The proposed model is found to be in excellent agreement with several experimental findings. The merit of the work is twofold in that it (1) accounts for the number and the strength of non-covalent cross-linking bonds, thus explaining the drastic reduction in stiffness upon water uptake, and (2) provides a method to characterize the micro-structural evolution of hydrogen-bond dominated networks. Consequently, the model can be used as a micro-structural design-guide to program the response of synthetic polymers.

Statement of Significance

Hydrogen-bond dominated biopolymer networks are found in insects and have a unique structure that allows a dramatic reduction of several orders of magnitude in stiffness upon hydration. Understanding the micro-structure of such networks is key in the fabrication of new biomimetic polymers with tunable mechanical properties. This work introduces a microscopically motivated model that explains the dramatic reduction in stiffness and quantifies the influence of key micro-structural quantities on the overall response. The model is validated through several experimental findings. The insights from this work motivate further attempts at the fabrication of new biomimetic polymers and serve as a micro-structural design guide that enables the programming of the elastic swelling-induced response.

Introduction

Resilin is an example of a rubber-like network dominated by hydrogen bonds that is found in the cuticle region of most insects [1], [2], [3]. Among other functions, resilin plays a major role in jumping [4], walking [5], and adhesion [6] mechanisms. Due to attractive properties such as high resilience, the capability of experiencing large deformations, and the ability to dramatically vary stiffness upon hydration and dehydration, resilin has been the subject of many investigations aiming to mimic its unique properties in synthetic materials [7], [8] which can be used in various applications [9].

The unusual elastomeric properties of resilin are highly regulated by water content [1], [3], [6], [8], [10], [11]. This stems from a unique molecular composition which differs from other structural proteins such as, e.g. elastin [12]. Resilin comprises a high proportion of hydrogen-bond forming and hydrophilic as well as polar amino acid residues (over 60 mol-%) with lysine and proline the dominating amino acids [9], [12], [13]. Both amino acid moieties provide high flexibility to resilin [13]. Furthermore, resilin contains about 6 mol-% tyrosine residues which form dityrosine and trityrosine cross-links, the ratio of which shows regional differences [14].

The distribution of hydrophilic and hydrophobic amino acids along the chain results in a segmented block copolymer type structure with predominantly hydrophilic segments, as shown in resilin from Drosophila [15]. The total sequence consists of three portions: exon 1 and exon 3, comprising 323 and 235 amino acids, respectively, functioning as the elastic constituents, and a comparatively short exon 2, with only 62 amino acids in between, which represents a typical cuticular chitin binding domain [15]. Short amino acid sequences within exon 1 and exon 2 are characteristic for their potential of secondary structure formation such as beta sheets and helices [16] and beta-turn conformation [13], [15]. The difference in the hydrophilic/hydrophobic comonomer ratio in exon 1 and exon 3 is considered resulting in special assembly features, i.e. preferences for fibrillar and micellar structures in the range 10–50 nm, respectively [15].

Mechanical data obtained with swollen resilin specimen of different insects [1], [3] and spectroscopic analysis of synthetic resilin [7] suggest that a network of ideally jointed chains serves as a good approximation of the elastic response. Additionally, the relatively broad range of elastic properties in resilin-based locomotion systems of insects [17], [18] indicates that reversible cross-links, which are based on intermolecular interactions such as hydrogen bonding and related supramolecular features, also play an important role. Specifically, experimental studies demonstrate that upon water uptake, the moduli of resilin networks can vary by several orders of magnitude while experiencing small to moderate volumetric deformations [6], [11], [19]. These observations cannot be explained by the pure swelling effect associated with rubbers, suggesting that there are additional mechanisms that contribute to the elasticity.

From a chemical viewpoint, the effects of hydration on a resilin network are well established. Water contained in resilin can be directly associated with the polypeptide by interacting with the peptide bond itself or with protein side groups (Fig. (1)); this has been referred to as “non-freezable” water [20]. Any water content that goes beyond this concentration is “free” water presumably within some sort of micro-pore structure [20], and finally resulting in the continuous aqueous phase of the swollen network. On the other hand, the removal of water content below a critical concentration required for complete solubilization of the polypeptide chains leads to the formation of intermolecular hydrogen bonds and may even result in beta-sheet structures [20]. A similar effect is found in other hydrogen bond dominated solids such as fibers or sheets made of cellulose and, to a certain extent, Nylon and wool [21], [22].

From a mechanical viewpoint, the change in properties of resilin, ranging from a hard and brittle material in the dehydrated state to a soft and highly elastic material in the swollen state can be understood as being related to the contribution of non-covalent, most likely hydrogen bond based cross-links between polypeptide chains. The amount of such temporary cross-links is correlated with the water content. Water molecules break intermolecular hydrogen bonds (Fig. 1), first acting similarly to a plasticizer [6], [8], [19], [20]. As the water content in resilin increases, the number of non-covalent cross-linking sites decreases, ultimately leading to a swollen resilin comprising only tyrosine-based covalent cross-links. Generally speaking, water molecules interact with polar groups of the resilin polypeptide [15], [16] and thus reduce the attraction between polymer chains, which in turn results in additional chain mobility and network flexibility.

The aim of this work is to derive a methodical microscopically motivated and statistical-mechanics based model that (1) captures the mechanisms of dissociation in non-covalent cross-linking bonds, (2) accounts for the micro-structure of hydrogen bond dominated polymer networks, (3) allows to determine the changes in entropy and free energy resulting from cross-link dissociation, (4) quantitatively explains the solubilization-induced reduction in stiffness, and (5) captures the overall elastic performance. We point out that several analyses of networks with transient cross-links have been carried out in the past [21], [22], [23], [24], [25], [26], [27], [28]. However, these works did not explicitly account for the micro-structure of the network, quantified the entropic gain and the free-energy as bonds break, or explained the origins of the drastic stiffness changes observed in biopolymer networks [6], [19], [29]. The energetically based microscopically motivated model introduced in this work addresses all of these phenomena and qualitatively and quantitatively agrees with various experimental findings.

Section snippets

A microscopically motivated model

In the following, we introduce a model that aims to capture the response of polymer networks with breakable cross-link bonds that is immersed in a liquid bath. The model we propose assumes that:

  • 1.

    The network is idealized as a network of freely jointed chains [29], where a chain is defined as a coiled segment connecting two cross-linking sites. It is emphasized that by making use of the freely-jointed chain model we neglect the valence angle and the rotational barriers between neighboring

The stiffness of hydrogen-bond dominated biopolymer networks

To validate the model, we compare its predictions to several experimental findings. The Young’s modulus at the tip of the seta of a ladybird beetle (Coccinella septempunctata) was measured to be E=7.2GPa and E=1.2MPa in the dehydrated and the hydrated states, respectively [6]. By assuming incompressibility (assumption (5)), the shear modulus G=E/3 can be obtained by taking φc=0,α=0.64·10-3, and clcrit=0.1, corresponding to the dissociation of almost all cross-links (ϕ=0.995). We point out that

The non-linear response of hydrogen-bond dominated biopolymer networks

The proposed model provides a systematic method to compute the macroscopic non-linear response of networks comprising non-covalent cross-link bonds. In this section, we compare the predictions of the proposed model to available experimental data on the stress-strain response under uniaxial tension of resilin from the tendons of Aeshna Grandis(cp=0.48) and Aeshna Cyanea(cp=0.45) [29]. This work infers that there are twice as many non-covalent cross-link bonds than chemical cross-links in the

Conclusions

In conclusion, we derived a robust thermodynamics-based framework that describes the influence of micro-structure on polymer networks that swell and deform under external loadings. The proposed model suggests that the breaking of non-covalent cross-links leads to a reduction in the effective chain-density and, consequently, an increase in entropy and a decrease in free energy. The model captures the softening response observed in arthropods, quantifies the number of broken cross-links, and

Acknowledgements

This work was supported in part by the National Science Foundation Materials Research Science and Engineering Center (IRG-3) DMR 1720256.

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      This phenomenon stems from the water-induced breaking of intermolecular hydrogen bonds in the semi-amorphous matrix. The dissociation of hydrogen bonds in the presence of water molecules has been widely discussed in previous works (Nissan, 1976a,b; Porter and Vollrath, 2008; Fu et al., 2011; Cohen and Eisenbach, 2019; Cohen et al., 2021b,a) and has been shown to lower the glass-transition temperature (Plaza et al., 2006; Elices et al., 2011). It is also worth mentioning that the presence of water molecules is not sufficient to disturb the hard crystalline domains (Yazawa et al., 2019, 2020).

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