Coarse-Grained Model of Collagen Molecules Using an Extended MARTINI Force Field

A multiscale investigation into the role of collagen-hyaluronan interface shear on the mechanical behaviour of collagen fibers in annulus fibrosus - Molecular dynamics-cohesive finite element-based study

Multi-directional deformation exhibited by annulus fibrosus (AF) is contributed by chemo-mechanical interactions among its biomolecular constituents' collagen type I (COL-I), collagen type II (COL-II), proteoglycans (aggrecan and hyaluronan) and water. However, the nature and role of such interactions on AF mechanics are unclear. This work employs a molecular dynamics-cohesive finite element-based multiscale approach to investigate role of COL-I-COL-II interchanging distribution and water concentration (WC) variations from outer annulus (OA) to inner annulus (IA) on collagen-hyaluronan (COL-HYL) interface shear, and the mechanisms by which interface shear impacts fibril sliding during collagen fiber deformation. At first, COL-HYL interface atomistic models are constructed by interchanging COL-I with COL-II and increasing COL-II and WC from 0 to 75%, and 65%-75% respectively. Thereafter, a multiscale approach is employed to develop representative volume elements (RVEs) of collagen fibers by incorporating COL-HYL shear as traction-separation behaviour at fibril-hyaluronan contact. Results show that increasing COL-II and WC increases interface stiffness from 0.6 GPa/nm to 1.2 GPa/nm and reduces interface strength from 155 MPa to 58 MPa from OA to IA, contributed by local hydration alterations. A stiffer and weaker interface enhances fibril sliding with increased straining at the contact - thereby contributing to reduction in modulus from 298 MPa to 198 MPa from OA to IA. Such reduction further contributes to softer mechanical response towards IA, as reported by earlier studies. Presented multiscale analysis provides deeper understanding of hierarchical structure-mechanics relationships in AF and can further aid in developing better substitutes for AF repair.

CADD, AI and ML in drug discovery: A comprehensive review

Computer-aided drug design (CADD) is an emerging field that has drawn a lot of interest because of its potential to expedite and lower the cost of the drug development process. Drug discovery research is expensive and time-consuming, and it frequently took 10-15 years for a drug to be commercially available. CADD has significantly impacted this area of research. Further, the combination of CADD with Artificial Intelligence (AI), Machine Learning (ML), and Deep Learning (DL) technologies to handle enormous amounts of biological data has reduced the time and cost associated with the drug development process. This review will discuss how CADD, AI, ML, and DL approaches help identify drug candidates and various other steps of the drug discovery process. It will also provide a detailed overview of the different in silico tools used and how these approaches interact.

Dynamic movement and turnover of extracellular matrices during tissue development and maintenance

Extracellular matrices (ECMs) are essential for the architecture and function of animal tissues. ECMs have been thought to be highly stable structures; however, too much stability of ECMs would hamper tissue remodelling required for organ development and maintenance. Regarding this conundrum, this article reviews multiple lines of evidence that ECMs are in fact rapidly moving and replacing components in diverse organisms including hydra, worms, flies, and vertebrates. Also discussed are how cells behave on/in such dynamic ECMs, how ECM dynamics contributes to embryogenesis and adult tissue homoeostasis, and what molecular mechanisms exist behind the dynamics. In addition, it is highlighted how cutting-edge technologies such as genome engineering, live imaging, and mathematical modelling have contributed to reveal the previously invisible dynamics of ECMs. The idea that ECMs are unchanging is to be changed, and ECM dynamics is emerging as a hitherto unrecognized critical factor for tissue development and maintenance.

Multiscale modeling of skin mechanical Behavior: Effect of dehydrating agent on Collagen's mechanical properties

The dermis, second layer of human skin, is mainly responsible for mechanical response of the skin. The unique viscoelastic nature of this layer arises from the characteristic hierarchical structure of collagen at various length scales. The effect of topical formulation on skin's mechanical properties of great importance for several personal-care applications. Understanding the transport of an active ingredient across skin layer and its effects on the structure of collagen assembly is crucial for successful design of these applications. In this study, we report a multiscale modelling framework mimicking the skin's mechanical behavior. The framework captures the details from the nanoscale (tropocollagen) to microscale (fibers). At first, atomistic molecular dynamics simulations (MDS) of tropocollagen (TC) molecules of various lengths (∼100 nm) were performed to obtain the molecular modulus of TC. The stress-strain response data obtained from these simulations, were utilized in macroscopic models of fibrils and fibers. The modulus obtained from the mentioned framework was in good agreement with earlier reported experimental data. Further, we have utilized this framework to show the effect of dehydrating agent on skin's mechanical response. The hydration effect is utilized in many anti-ageing strategies to improve the overall mechanical property of skin. We showed that on incorporation of hydrating agent, the collagen structure changes significantly at molecular scale which effects the overall response of the skin at macroscopic scale. The reported multiscale framework can further be explored to gain insights into interlinked properties of collagen at much larger scales without extensive molecular simulations and detailed experiments.

Probing the alignment-dependent mechanical behaviors and time-evolutional aligning process of collagen scaffolds

Efficiently manipulating and reproducing collagen (COL) alignment in vitro remains challenging because many of the fundamental mechanisms underlying and guiding the alignment process are not known. We reconcile experiments and coarse-grained molecular dynamics simulations to investigate the mechanical behaviors of a growing COL scaffold and assay how changes in fiber alignment and various cross-linking densities impact their alignment dynamics under shear flow. We find higher cross-link densities and alignment levels significantly enhance the apparent tensile/shear moduli and strength of a bulk COL system, suggesting potential measures to facilitate the design of stronger COL based materials. Since fibril alignment plays a key factor in scaffold mechanics, we next investigate the molecular mechanism behind fibril alignment with Couette flow by computationally investigating the effects of COL's structural properties such as chain lengths, number of chains, tethering conditions, and initial COL conformations on the COL's final alignment level. Our computations suggest that longer chain lengths, more chains, greater amounts of tethering, and initial anisotropic COL conformations benefit the final alignment, but the effect of chain lengths may be more dominant over other factors. These results provide important parameters for consideration in manufacturing COL-based scaffolds where alignment and cross-linking are necessary for regulating performance.

A rethinking of collagen as tough biomaterials in meat packaging: assembly from native to synthetic

Due to the high moisture-associated typical rheology and the changeable and harsh processing conditions in the production process, packaging materials for meat products have higher requirements including a sufficient mechanical strength and proper ductility. Collagen, a highly conserved structural protein consisting of a triple helix of Gly-X-Y repeats, has been proved to be suitable packaging material for meat products. The treated animal digestive tract (i.e. the casing) is the perfect natural packaging material for wrapping meat into sausage. Its thin walls, strong toughness and impact resistance make it the oldest and best edible meat packaging. Collagen casing is another wisdom of meat packaging, which is made by collagen fibers from hide skin, presenting a rapid growth in casing market. To strengthen mechanical strength and barrier behaviors of collagen-based packaging materials, different physical, chemical, and biological cross-linking methods are springing up exuberantly, as well as a variety of reinforcement approaches including nanotechnology. In addition, the rapid development of biomimetic technology also provides a good research idea and means for the promotion of collagen's assembly and relevant mechanical properties. This review can offer some reference on fundamental theory and practical application of collagenous materials in meat products.

Impact of collagen-like peptide (CLP) heterotrimeric triple helix design on helical thermal stability and hierarchical assembly: a coarse-grained molecular dynamics simulation study

Collagen-like peptides (CLP) are multifunctional materials garnering a lot of recent interest from the biomaterials community due to their hierarchical assembly and tunable physicochemical properties. In this work, we present a computational study that links the design of CLP heterotrimers to the thermal stability of the triple helix and their self-assembly into fibrillar aggregates and percolated networks. Unlike homotrimeric helices, the CLP heterotrimeric triple helices in this study are made of CLP strands of different chain lengths that result in 'sticky' ends with available hydrogen bonding groups. These 'sticky' ends at one end or both ends of the CLP heterotrimer then facilitate inter-helix hydrogen bonding leading to self-assembly into fibrils (clusters) and percolated networks. We consider the cases of three sticky end lengths - two, four, and six repeat units - present entirely on one end or split between two ends of the CLP heterotrimer. We observe in CLP heterotrimer melting curves generated using coarse grained Langevin dynamics simulations at low CLP concentration that increasing sticky end length results in lower melting temperatures for both one and two sticky ended CLP designs. At higher CLP concentrations, we observe non-monotonic trends in cluster sizes with increasing sticky end length with one sticky end but not for two sticky ends with the same number of available hydrogen bonding groups as the one sticky end; this nonmonotonicity stems from the formation of turn structures stabilized by hydrogen bonds at the single, sticky end for sticky end lengths greater than four repeat units. With increasing CLP concentration, heterotrimers also form percolated networks with increasing sticky end length with a minimum sticky end length of four repeat units required to observe percolation. Overall, this work informs the design of thermoresponsive, peptide-based biomaterials with desired morphologies using strand length and dispersity as a handle for tuning thermal stability and formation of supramolecular structures.

Devising Bone Molecular Models at the Nanoscale: From Usual Mineralized Collagen Fibrils to the First Bone Fibers Including Hydroxyapatite in the Extra-Fibrillar Volume

At the molecular scale, bone is mainly constituted of type-I collagen, hydroxyapatite, and water. Different fractions of these constituents compose different composite materials that exhibit different mechanical properties at the nanoscale, where the bone is characterized as a fiber, i.e., a bundle of mineralized collagen fibrils surrounded by water and hydroxyapatite in the extra-fibrillar volume. The literature presents only models that resemble mineralized collagen fibrils, including hydroxyapatite in the intra-fibrillar volume only, and lacks a detailed prescription on how to devise such models. Here, we present all-atom bone molecular models at the nanoscale, which, differently from previous bone models, include hydroxyapatite both in the intra-fibrillar volume and in the extra-fibrillar volume, resembling fibers in bones. Our main goal is to provide a detailed prescription on how to devise such models with different fractions of the constituents, and for that reason, we have made step-by-step scripts and files for reproducing these models available. To validate the models, we assessed their elastic properties by performing molecular dynamics simulations that resemble tensile tests, and compared the computed values against the literature (both experimental and computational results). Our results corroborate previous findings, as Young’s Modulus values increase with higher fractions of hydroxyapatite, revealing all-atom bone models that include hydroxyapatite in both the intra-fibrillar volume and in the extra-fibrillar volume as a path towards realistic bone modeling at the nanoscale.

Multiscale modelling of the extracellular matrix

The extracellular matrix is a complex three-dimensional network of molecules that provides cells with a complex microenvironment. The major constituents of the extracellular matrix such as collagen, elastin and associated proteins form supramolecular assemblies contributing to its physicochemical properties and organization. The structure of proteins and their supramolecular assemblies such as fibrils have been studied at the atomic level (e.g., by X-ray crystallography, Nuclear Magnetic Resonance and cryo-Electron Microscopy) or at the microscopic scale. However, many protein complexes are too large to be studied at the atomic level and too small to be studied by microscopy. Most extracellular matrix components fall into this intermediate scale, so-called the mesoscopic scale, preventing their detailed characterization. Simulation and modelling are some of the few powerful and promising approaches that can deepen our understanding of mesoscale systems. We have developed a set of modelling tools to study the self-organization of the extracellular matrix and large motion of macromolecules at the mesoscale level by taking advantage of the dynamics of articulated rigid bodies as a mean to study a larger range of motions at the cost of atomic resolution.

Design and Production of Customizable and Highly Aligned Fibrillar Collagen Scaffolds

The ability to fabricate anisotropic collagenous materials rapidly and reproducibly has remained elusive despite decades of research. Balancing the natural propensity of monomeric collagen (COL) to spontaneously polymerize in vitro with the mild processing conditions needed to maintain its native substructure upon polymerization introduces challenges that are not easily amenable with off-the-shelf instrumentation. To overcome these challenges, we have designed a platform that simultaneously aligns type I COL fibrils under mild shear flow and builds up the material through layer-by-layer assembly. We explored the mechanisms propagating fibril alignment, targeting experimental variables such as shear rate, viscosity, and time. Coarse-grained molecular dynamics simulations were also employed to help understand how initial reaction conditions including chain length, indicative of initial polymerization, and chain density, indicative of concentration, in the reaction environment impact fibril growth and alignment. When taken together, the mechanistic insights gleaned from these studies inspired the design, iteration, fabrication, and then customization of the fibrous collagenous materials, illustrating a platform material that can be readily adapted to future tissue engineering applications.

Influence of Hydroxyproline on Mechanical Behavior of Collagen Mimetic Proteins Under Fraying Deformation-Molecular Dynamics Investigations

Molecular dynamics modeling is used to simulate, model, and analyze mechanical deformation behavior and predictive properties of three different synthetic collagen proteins obtained from RSC-PDB, 1BKV, 3A08, and 2CUO, with varying concentrations of hydroxyproline (HYP). Hydroxyproline is credited with providing structural support for the collagen protein molecules. Hydroxyproline's influence on these three synthetic collagen proteins' mechanical deformation behavior and predictive properties is investigated in this paper. A detailed study and inference of the protein's mechanical characteristics associated with HYP content are investigated through fraying deformation behavior. A calculated Gibbs free energy value (ΔG) of each polypeptide α chain that corresponds with a complete unfolding of a single polypeptide α-chain from a triple-helical protein is obtained with umbrella sampling. The force needed for complete separation of the polypeptide α-chain from the triple-helical protein is analyzed for proteins to understand the influence of HYP concentration and is discussed in this paper. Along with a difference in ΔG, different unfolding pathways for the molecule and individual chains are observed. The correlation between the fraying deformation mechanical characteristics and the collagen proteins' hydroxyproline content is provided in this study via the three collagen proteins' resulting binding energies.

Combining simulations and experiments for the molecular engineering of multifunctional collagen mimetic peptide-based materials

Assembling peptides allow the creation of structurally complex materials, where amino acid selection influences resulting properties. We present a synergistic approach of experiments and simulations for examining the influence of natural and non-natural amino acid substitutions via incorporation of charged residues and a reactive handle on the thermal stability and assembly of multifunctional collagen mimetic peptides (CMPs). Experimentally, we observed inclusion of charged residues significantly decreased the melting temperature of CMP triple helices with further destabilization upon inclusion of the reactive handle. Atomistic simulations of a single CMP triple helix in explicit water showed increased residue-level and helical structural fluctuations caused by the inclusion of the reactive handle; however, these atomistic simulations cannot be used to predict changes in CMP melting transition. Coarse-grained (CG) simulations of CMPs at experimentally relevant solution conditions, showed, qualitatively, the same trends as experiments in CMP melting transition temperature with CMP design. These simulations show that when charged residues are included electrostatic repulsions significantly destabilize the CMP triple helix and that an additional inclusion of a reactive handle does not significantly change the melting transition. Based on findings from both experiments and simulations, the sequence design was refined for increased CMP triple helix thermal stability, and the reactive handle was utilized for the incorporation of the assembled CMPs within covalently crosslinked hydrogels. Overall, a unique approach was established for predicting stability of CMP triple helices for various sequences prior to synthesis, providing molecular insights for sequence design towards the creation of bulk nanostructured soft biomaterials.

Discovery of Self-Assembling π-Conjugated Peptides by Active Learning-Directed Coarse-Grained Molecular Simulation

Electronically active organic molecules have demonstrated great promise as novel soft materials for energy harvesting and transport. Self-assembled nanoaggregates formed from π-conjugated oligopeptides composed of an aromatic core flanked by oligopeptide wings offer emergent optoelectronic properties within a water-soluble and biocompatible substrate. Nanoaggregate properties can be controlled by tuning core chemistry and peptide composition, but the sequence-structure-function relations remain poorly characterized. In this work, we employ coarse-grained molecular dynamics simulations within an active learning protocol employing deep representational learning and Bayesian optimization to efficiently identify molecules capable of assembling pseudo-1D nanoaggregates with good stacking of the electronically active π-cores. We consider the DXXX-OPV3-XXXD oligopeptide family, where D is an Asp residue and OPV3 is an oligophenylenevinylene oligomer (1,4-distyrylbenzene), to identify the top performing XXX tripeptides within all 20³ = 8000 possible sequences. By direct simulation of only 2.3% of this space, we identify molecules predicted to exhibit superior assembly relative to those reported in prior work. Spectral clustering of the top candidates reveals new design rules governing assembly. This work establishes new understanding of DXXX-OPV3-XXXD assembly, identifies promising new candidates for experimental testing, and presents a computational design platform that can be generically extended to other peptide-based and peptide-like systems.

Charge-dependent interactions of monomeric and filamentous actin with lipid bilayers

The cytoskeletal protein actin polymerizes into filaments that are essential for the mechanical stability of mammalian cells. In vitro experiments showed that direct interactions between actin filaments and lipid bilayers are possible and that the net charge of the bilayer as well as the presence of divalent ions in the buffer play an important role. In vivo, colocalization of actin filaments and divalent ions are suppressed, and cells rely on linker proteins to connect the plasma membrane to the actin network. Little is known, however, about why this is the case and what microscopic interactions are important. A deeper understanding is highly beneficial, first, to obtain understanding in the biological design of cells and, second, as a possible basis for the building of artificial cortices for the stabilization of synthetic cells. Here, we report the results of coarse-grained molecular dynamics simulations of monomeric and filamentous actin in the vicinity of differently charged lipid bilayers. We observe that charges on the lipid head groups strongly determine the ability of actin to adsorb to the bilayer. The inclusion of divalent ions leads to a reversal of the binding affinity. Our in silico results are validated experimentally by reconstitution assays with actin on lipid bilayer membranes and provide a molecular-level understanding of the actin-membrane interaction.

Temporally Coarse-Grained All-Atom Molecular Dynamics Achieved via Stochastic Padé Approximants

A Padé approximant scheme for realizing the discrete-time evolution of the state of a many-atom system is introduced. This temporal coarse-graining scheme accounts for the underlying Newtonian physics and avoids the need for construction of spatially coarse-grained variables. Newtonian physics is incorporated through short molecular dynamics simulations at the beginning of each of the large coarse-grained timesteps. The balance between stochastic and coherent dynamics expressed by many-atom systems is captured via incorporation of the Ito formula into a Padé approximant for the time dependence of individual atom positions over large timesteps. Since the time for a many-atom system to express a characteristic ensemble of atomic velocity fluctuations is typically short relative to the characteristic time of large-scale atomic displacements, a computationally efficient and accurate temporal coarse-graining of the atom-resolved Newtonian dynamics is formulated, denoted all-atom Padé-Ito molecular dynamics (APIMD). Evolution of the system over a time step much longer than that required for standard molecular dynamics (MD) is achieved via incorporation of information from the short MD simulations into a Padé approximant extrapolation in time. The extrapolated atomic configuration is subjected to energy minimization and, when needed, thermal equilibration so as to avoid occasional unphysical close encounters deriving from the Padé approximant extrapolation and to represent configurations appropriate for the temperature of interest. APIMD is implemented and tested via comparison with traditional MD simulations of five phenomena: (1) pertussis toxin subunit deformation, (2) structural transition in a T = 1 capsid-like structure of HPV16 L1 protein, (3) coalescence of argon nanodroplets, and structural transitions in dialanine in (4) vacuum, and (5) water. Accuracy of APIMD is demonstrated using semimicroscopic descriptors (rmsd, radius of gyration, residue-residue contact maps, and densities) and the free energy. Significant computational acceleration relative to traditional molecular dynamics is illustrated.

Probing mechanical properties and failure mechanisms of fibrils of self-assembling peptides

Self-assembling peptides (SAPs) are a promising class of biomaterials amenable to easy molecular design and functionalization. Despite their increasing usage in regenerative medicine, a detailed analysis of their biomechanics at the nanoscale level is still missing. In this work, we propose and validate, in all-atom dynamics, a coarse-grained model to elucidate strain distribution, failure mechanisms and biomechanical effects of functionalization of two SAPs when subjected to both axial stretching and bending forces. We highlight different failure mechanisms for fibril seeds and fibrils, as well as the negligible contribution of the chosen functional motif to the overall system rupture. This approach could lay the basis for the development of "more" coarse-grained models in the long pathway connecting SAP sequences and hydrogel mechanical properties.

Methacrylate Coatings for Titanium Surfaces to Optimize Biocompatibility

Currently, there are more than 1.5 million knee and hip replacement procedures carried out in the United States. Implants have a 10-15-year lifespan with up to 30% of revision surgeries showing complications with osteomyelitis. Titanium and titanium alloys are the favored implant materials because they are lightweight and have high mechanical strength. However, this increased strength can be associated with decreased bone density around the implant, leading to implant loosening and failure. To avoid this, current strategies include plasma-spraying titanium surfaces and foaming titanium. Both techniques give the titanium a rough and irregular finish that improves biocompatibility. Recently, researchers have also sought to surface-conjugate proteins to titanium to induce osteointegration. Cell adhesion-promoting proteins can be conjugated to methacrylate groups and crosslinked using a variety of methods. Methacrylated proteins can be conjugated to titanium surfaces through atom transfer radical polymerization (ATRP). However, surface conjugation of proteins increases biocompatibility non-specifically to bone cells, adding to the risk of biofouling which may result in osteomyelitis that causes implant failure. In this work, we analyze the factors contributing to biofouling when coating titanium to improve biocompatibility, and design an experimental scheme to evaluate optimal coating parameters.

Conformational preferences and phase behavior of intrinsically disordered low complexity sequences: insights from multiscale simulations

While many proteins and protein regions utilize a complex repertoire of amino acids to achieve their biological function, a subset of protein sequences are enriched in a reduced set of amino acids. These so-called low complexity (LC) sequences, specifically intrinsically disordered variants of LC sequences, have been the focus of recent investigations owing to their roles in a range of biological functions, specifically phase separation. Computational studies of LC sequences have provided rich insights into their behavior both as individual proteins in dilute solutions and as the drivers and modulators of higher-order assemblies. Here, we review how simulations performed across distinct resolutions have provided different types of insights into the biological role of LC sequences.

Steered molecular dynamics characterization of the elastic modulus and deformation mechanisms of single natural tropocollagen molecules

Collagen is a common structural protein, providing mechanical integrity for various vertebrate connective tissues such as cartilage and bone. The mechanical behaviours of these tissues under physical stimulations are controlled by the hierarchical structure of collagen and its interactions with other extracellular matrix molecules. However, the mechanical properties and deformation mechanisms of natural collagen under physiological loading rates at the molecular level are not fully understood. In this study, comprehensive steered molecular dynamics (SMD) simulations were performed on the 2nd intact overlap region (d2ol) and the 2nd intact D-period (d2olgp) of an in-situ characterized collagen molecule, under a large range of strain rates (6.5 × 10⁶% s^-1 to 1.3 × 10¹²% s^-1). The results show that, depending on the applied strain rates, tropocollagen molecules unfold in different ways. Particularly, at high and intermediate strain rates, the number of inter-chain hydrogen bonds decreases rapidly even at small deformations, leading to a dramatic increase in the force. This results in an increase in the estimated Young's modulus of collagen triple helices as the deformation rate goes up, which, together with the nonlinear mechanical behaviour, explains the broad range of the Young's modulus for collagen model peptides reported in earlier SMD studies. Atomistic-level analyses indicate that the elastic modulus of single tropocollagen molecules decreases as the strain rate becomes smaller. However, for strain rates below 1.3 × 10⁸% s^-1, the tangent Young's modulus of d2ol (d2olgp) converges to approximately 3.2 GPa (3.4 GPa), at the strain of 10.5% (12%) when the segment is fully uncrimped. Furthermore, for strain rates under 1.3 × 10⁸% s^-1, d2ol and d2olgp show identical deformation mechanisms (unwinding, uncoiling and backbone stretching), but the corresponding strain ranges are different. This study will aid in future studies on characterizing the mechanical properties of collagen molecules and collagen-like peptides by indicating the proper pulling strain rates and how to determine the suitable strain range used for evaluating the elastic modulus.

Materials-by-Design: Computation, Synthesis, and Characterization from Atoms to Structures

In the 50 years that succeeded Richard Feynman's exposition of the idea that there is "plenty of room at the bottom" for manipulating individual atoms for the synthesis and manufacturing processing of materials, the materials-by-design paradigm is being developed gradually through synergistic integration of experimental material synthesis and characterization with predictive computational modeling and optimization. This paper reviews how this paradigm creates the possibility to develop materials according to specific, rational designs from the molecular to the macroscopic scale. We discuss promising techniques in experimental small-scale material synthesis and large-scale fabrication methods to manipulate atomistic or macroscale structures, which can be designed by computational modeling. These include recombinant protein technology to produce peptides and proteins with tailored sequences encoded by recombinant DNA, self-assembly processes induced by conformational transition of proteins, additive manufacturing for designing complex structures, and qualitative and quantitative characterization of materials at different length scales. We describe important material characterization techniques using numerous methods of spectroscopy and microscopy. We detail numerous multi-scale computational modeling techniques that complements these experimental techniques: DFT at the atomistic scale; fully atomistic and coarse-grain molecular dynamics at the molecular to mesoscale; continuum modeling at the macroscale. Additionally, we present case studies that utilize experimental and computational approaches in an integrated manner to broaden our understanding of the properties of two-dimensional materials and materials based on silk and silk-elastin-like proteins.

Multiscale modeling of keratin, collagen, elastin and related human diseases: Perspectives from atomistic to coarse-grained molecular dynamics simulations

Scleroproteins are an important category of proteins within the human body that adopt filamentous, elongated conformations in contrast with typical globular proteins. These include keratin, collagen, and elastin, which often serve a common mechanical function in structural support of cells and tissues. Genetic mutations alter these proteins, disrupting their functions and causing diseases. Computational characterization of these mutations has proven to be extremely valuable in identifying the intricate structure-function relationships of scleroproteins from the molecular scale up, especially if combined with multiscale experimental analysis and the synthesis of model proteins to test specific structure-function relationships. In this work, we review numerous critical diseases that are related to keratin, collagen, and elastin, and through several case studies, we propose ways of extensively utilizing multiscale modeling, from atomistic to coarse-grained molecular dynamics simulations, to uncover the molecular origins for some of these diseases and to aid in the development of novel cures and therapies. As case studies, we examine the effects of the genetic disease Epidermolytic Hyperkeratosis (EHK) on the structure and aggregation of keratins 1 and 10; we propose models to understand the diseases of Osteogenesis Imperfecta (OI) and Alport syndrome (AS) that affect the mechanical and aggregation properties of collagen; and we develop atomistic molecular dynamics and elastic network models of elastin to determine the role of mutations in diseases such as Cutis Laxa and Supravalvular Aortic Stenosis on elastin's structure and molecular conformational motions and implications for assembly.

Design of Polyphosphate Inhibitors: A Molecular Dynamics Investigation on Polyethylene Glycol-Linked Cationic Binding Groups

Inorganic polyphosphate (polyP) released by human platelets has recently been shown to activate blood clotting and identified as a potential target for the development of novel antithrombotics. Recent studies have shown that polymers with cationic binding groups (CBGs) inhibit polyP and attenuate thrombosis. However, a good molecular-level understanding of the binding mechanism is lacking for further drug development. While molecular dynamics (MD) simulation can provide molecule-level information, the time scale required to simulate these large biomacromolecules makes classical MD simulation impractical. To overcome this challenge, we employed metadynamics simulations with both all-atom and coarse-grained force fields. The force field parameters for polyethylene glycol (PEG) conjugated CBGs and polyP were developed to carry out coarse-grained MD simulations, which enabled simulations of these large biomacromolecules in a reasonable time scale. We found that the length of the PEG tail does not impact the interaction between the (PEG) _n-CBG and polyP. As expected, increasing the number of the charged tertiary amine groups in the head group strengthens its binding to polyP. Our simulation shows that (PEG) _n-CBG initially form aggregates, mostly with the PEG in the core and the hydrophilic CBG groups pointing toward water; then the aggregates approach the polyP and sandwich the polyP to form a complex. We found that the binding of (PEG) _n-CBG remains intact against various lengths of polyP. Binding thermodynamics for two of the (PEG) _n-CBG/polyP systems simulated were measured by isothermal titration calorimetry to confirm the key finding of the simulations that the length PEG tail does not influence ligand binding to polyP.

Theory of wavelet-based coarse-graining hierarchies for molecular dynamics

We present a multiresolution approach to compressing the degrees of freedom and potentials associated with molecular dynamics, such as the bond potentials. The approach suggests a systematic way to accelerate large-scale molecular simulations with more than two levels of coarse graining, particularly applications of polymeric materials. In particular, we derive explicit models for (arbitrarily large) linear (homo)polymers and iterative methods to compute large-scale wavelet decompositions from fragment solutions. This approach does not require explicit preparation of atomistic-to-coarse-grained mappings, but instead uses the theory of diffusion wavelets for graph Laplacians to develop system-specific mappings. Our methodology leads to a hierarchy of system-specific coarse-grained degrees of freedom that provides a conceptually clear and mathematically rigorous framework for modeling chemical systems at relevant model scales. The approach is capable of automatically generating as many coarse-grained model scales as necessary, that is, to go beyond the two scales in conventional coarse-grained strategies; furthermore, the wavelet-based coarse-grained models explicitly link time and length scales. Furthermore, a straightforward method for the reintroduction of omitted degrees of freedom is presented, which plays a major role in maintaining model fidelity in long-time simulations and in capturing emergent behaviors.

Persistence length of collagen molecules based on nonlocal viscoelastic model

Persistence length is one of the most interesting properties of a molecular chain, which is used to describe the stiffness of a molecule. The experimentally measured values of the persistence length of the collagen molecule are widely scattered from 14 to 180 nm. Therefore, an alternative approach is highly desirable to predict the persistence length of a molecule and also to explain the experimental results. In this paper, a nonlocal viscoelastic model is developed to obtain the persistence length of the collagen molecules in solvent. A new explicit formula is proposed for the persistence length of the molecule with the consideration of the small-scale effect, viscoelastic properties of the molecule, loading frequency, and viscosity of the solvent. The presented model indicates that there exists a range of molecule lengths in which the persistence length strongly depends on the frequency and spatial mode of applied loads, small-scale effect, and viscoelastic properties of the collagen.

High-Resolution Insights into the Stepwise Self-Assembly of Nanofiber from Bioactive Peptides

Peptide self-assembly has a profound biological significance since self-assembled bioactive peptides are gifted with improved bioactivity as well as life-span. In this study, peptide self-assembly was investigated using a therapeutic peptide, PTP-7S (EENFLGALFKALSKLL). Combining experiments of atomic force microscopy (AFM), circular dichroism (CD), and 8-anilino-1-naphthalenesulfonic acid (ANS) fluorescence spectra, PTP-7S showed the α-helical structure and was found self-assembling into nanofibers in solution. Relying on the coarse-grained (CG) dynamic simulations, the self-assembling of PTP-7S was revealed as a stepwise process that peptide monomers first clustered into peptide-assembling units (PUs) with charged surface, and then the PUs integrated together to construct nanofibril aggregates. Different roles of the nonbonded driving forces did play in the two phases: the hydrophobic force and electrostatic interaction acted as the predominant motivations in the formation of PUs and nanofiber, respectively. Moreover, the electrostatic interaction helped to guide the longitudinal growth of peptide nanofibers. A sequence principle is proposed for peptide self-assembling in aqueous solution: a balance of the counter charges and sufficient hydrophobicity degree. The self-assembled PTP-7S displayed good anticancer activity, proteases resistance, and sustained drug-release, showing a great potential for clinical application. This study reveals the molecular mechanism in explaining PTP-7S self-assembly and it is beneficial for future innovation of the self-assembled bioactive peptides.

Looking "Under the Hood" of Cellular Mechanotransduction with Computational Tools: A Systems Biomechanics Approach across Multiple Scales

Signal modulation has been developed in living cells throughout evolution to promote utilizing the same machinery for multiple cellular functions. Chemical and mechanical modules of signal transmission and transduction are interconnected and necessary for organ development and growth. However, due to the high complexity of the intercommunication of physical intracellular connections with biochemical pathways, there are many missing details in our overall understanding of mechanotransduction processes, i.e., the process by which mechanical signals are converted to biochemical cascades. Cell-matrix adhesions are mechanically coupled to the nucleus through the cytoskeleton. This modulated and tightly integrated network mediates the transmission of mechanochemical signals from the extracellular matrix to the nucleus. Various experimental and computational techniques have been utilized to understand the basic mechanisms of mechanotransduction, yet many aspects have remained elusive. Recently, in silico experiments have made important contributions to the field of mechanobiology. Herein, computational modeling efforts devoted to understanding integrin-mediated mechanotransduction pathways are reviewed, and an outlook is presented for future directions toward using suitable computational approaches and developing novel techniques for addressing important questions in the field of mechanotransduction.

Mechanical response and deformation mechanics of Type IV pili investigated using steered coarse-grained molecular dynamics simulation

Type IV pili are long filamentous structures on the surface of bacteria, which can be rapidly assembled or disassembled with pilin subunits by molecular motors. They can generate force during retraction and are involved in many bacterial functions. Steered molecular dynamics simulations with coarse-grained MARTINI models are carried out to investigate the mechanical behaviors of pili under tension. Our study is the first to report a Young's modulus of 0.80±0.07GPa and a spring constant of 1294.6±116.5kJmol^-1nm^-2 for pilus. Our results show the mechanical responses of pili are different from those described by the worm-like chain model and the van der Waal's interactions play a critical role in the mechanical responses. Moreover, the effects of pulling rates and virtual spring constants of pilus on Young's modulus are studied and two distinct morphological stages with the conformational changes appear during the extension of pilus are observed. This work provide insight into the mechanics and the deformation mechanism of pilus assembly.

Theory and Simulation of Cholesteric Film Formation Flows of Dilute Collagen Solutions

Dilute isotropic collagen solutions are usually flow processed into monodomain chiral nematic thin films for obtaining highly ordered materials by a multistep process that starts with complex inhomogeneous flow kinematics. Here we present rigorous theory and simulation of the initial precursors during flow steps in cholesteric collagen film formation. We first extract the molecular shape parameter and rotational diffusivity from previously reported simple shear data of dilute collagen solutions, where the former leads the reactive parameter (tumbling function) which determines the net effect of vorticity and strain rate on the average orientation and where the latter establishes the intensity of strain required for flow-birefringence, both crucial quantities for controlled film formation flow. We find that the tumbling function is similar to those of rod-like lyotropic liquid crystalline polymers and hence it is predicted that they would tumble in the ordered high concentration state leading to flow-induced texturing. The previously reported experimental data is well fitted with rotational diffusivities whose order of magnitude is consistent to those of other biomacromolecules. We then investigate the response of the tensor order parameter to complex flow kinematics, ranging from pure vorticity, through simple shear, to extensional flow, as may arise in typical flow casting and film flows. The chosen control variable to produce precursor cholesteric films is the director or average orientation, since the nematic order is set close to typical values found in concentrated cholesteric type I collagen solutions. Using the efficient four-roll mill kinematics, we summarize the para-nematic structure-flow process diagram in terms of the director orientation and flow type. Using analysis and computation, we provide a parametric envelope that is necessary to eventually produce well-aligned cholesteric films. We conclude that extensional flow is an essential ingredient of well-ordered film precursors with required Deborah numbers on the order of unity.

Steered molecular dynamics analysis of the role of cofilin in increasing the flexibility of actin filaments

Cofilin is one of the most essential regulatory proteins and participates in the process of disassembling actin filaments. Cofilin induces conformational changes to actin filaments, and both the bending and torsional rigidity of the filament. In this study, we investigate the effects of cofilin on the mechanical properties of actin filaments using computational methods. Three models defined by their number of bound cofilins are constructed using coarse-grained MARTINI force field, and they are then extended with steered molecular dynamics simulation. After obtaining the stress-strain curves of the models, we calculate their Young's moduli and other mechanical properties that have not yet been determined for actin filaments. We analyze the cause of the different behaviors of the three models based on their atomistic geometrical differences. Finally, it is demonstrated that cofilin binding causes changes in the distances, angles, and stabilities of the residues in actin filaments.

Characterization of the viscoelastic behavior of a simplified collagen micro-fibril based on molecular dynamics simulations

Collagen fibril is a major component of connective tissues such as bone, tendon, blood vessels, and skin. The mechanical properties of this highly hierarchical structure are greatly influenced by the presence of covalent cross-links between individual collagen molecules. This study investigates the viscoelastic behavior of a collagen lysine-lysine cross-link based on creep simulations with applied forces in the range or 10 to 2000pN using steered molecular dynamics (SMD). The viscoelastic model of the cross-link was combined with a system composed by two segments of adjacent collagen molecules hence representing a reduced viscoelastic model for a simplified micro-fibril. It was found that the collagen micro-fibril assembly had a steady-state Young׳s modulus ranging from 2.24 to 3.27GPa, which is in agreement with reported experimental measurements. The propagation of longitudinal force wave along the molecule was implemented by adding a delay element to the model. The force wave speed was found to be correlated with the speed of one-dimensional elastic waves in rods. The presented reduced model with three degrees of freedom can serve as a building block for developing models of the next level of hierarchy, i.e., a collagen fibril.

Investigation of ethanol infiltration into demineralized dentin collagen fibrils using molecular dynamics simulations

The purpose of this study is to investigate the interaction of neat ethanol with bound and non-bound water in completely demineralized dentin that is fully hydrated, using molecular dynamics (MD) simulation method. The key to creating ideal resin-dentin bonds is the removal of residual free water layers and its replacement by ethanol solvent in which resin monomers are soluble, using the ethanol wet-bonding technique. The test null hypotheses were that ethanol cannot remove any collagen-bound water, and that ethanol cannot infiltrate into the spacing between collagen triple helix due to narrow interlayer spacing. Collagen fibrillar structures of overlap and gap regions were constructed by aligning the collagen triple helix of infinite length in hexagonal packing. Three layers of the water molecules were specified as the layers of 0.15-0.22nm, 0.22-0.43nm and 0.43-0.63nm from collagen atoms by investigating the water distribution surrounding collagen molecules. Our simulation results show that ethanol molecules infiltrated into the intermolecular spacing in the gap region, which increased due to the lateral shrinkage of the collagen structures in contact with ethanol solution, while there was no ethanol infiltration observed in the overlap region. Infiltrated ethanol molecules in the gap region removed residual water molecules via modifying mostly the third water layer (50% decrease), which would be considered as a loosely-bound water layer. The first and second hydration layers, which would be considered as tightly bound water layers, were not removed by the ethanol molecules, thus maintaining the helical structures of the collagen molecules.

MARTINI Coarse-Grained Model of Triton TX-100 in Pure DPPC Monolayer and Bilayer Interfaces

The coarse-grained MARTINI model of Triton TX-100 has been validated by direct comparison of the experimental and calculated area increase in pure DPPC lipid bilayers and monolayers at water/air interfaces in the presence of surfactant and by comparison of electron density profiles calculated with more detailed atomistic models based on the CHARMM force field. Bilayer simulations have been performed and compared with monolayers and with atomistic models. The validated CG model has been employed to study the phase separation of TX-100 molecules in lipid bilayers and the effect of the lipid bilayer curvature.

Investigation of mechanisms of viscoelastic behavior of collagen molecule

Unique mechanical properties of collagen molecule make it one of the most important and abundant proteins in animals. Many tissues such as connective tissues rely on these properties to function properly. In the past decade, molecular dynamics (MD) simulations have been used extensively to study the mechanical behavior of molecules. For collagen, MD simulations were primarily used to determine its elastic properties. In this study, constant force steered MD simulations were used to perform creep tests on collagen molecule segments. The mechanical behavior of the segments, with lengths of approximately 20 (1X), 38 (2X), 74 (4X), and 290 nm (16X), was characterized using a quasi-linear model to describe the observed viscoelastic responses. To investigate the mechanisms of the viscoelastic behavior, hydrogen bonds (H-bonds) rupture/formation time history of the segments were analyzed and it was shown that the formation growth rate of H-bonds in the system is correlated with the creep growth rate of the segment (β=2.41βH). In addition, a linear relationship between H-bonds formation growth rate and the length of the segment was quantified. Based on these findings, a general viscoelastic model was developed and verified here, using the smallest segment as a building block, the viscoelastic properties of larger segments could be predicted. In addition, the effect of temperature control methods on the mechanical properties were studied, and it was shown that application of Langevin Dynamics had adverse effect on these properties while the Lowe-Anderson method was shown to be more appropriate for this application. This study provides information that is essential for multi-scale modeling of collagen fibrils using a bottom-up approach.

The materials science of collagen

Collagen is the principal biopolymer in the extracellular matrix of both vertebrates and invertebrates. It is produced in specialized cells (fibroblasts) and extracted into the body by a series of intra and extracellular steps. It is prevalent in connective tissues, and the arrangement of collagen determines the mechanical response. In biomineralized materials, its fraction and spatial distribution provide the necessary toughness and anisotropy. We review the structure of collagen, with emphasis on its hierarchical arrangement, and present constitutive equations that describe its mechanical response, classified into three groups: hyperelastic macroscopic models based on strain energy in which strain energy functions are developed; macroscopic mathematical fits with a nonlinear constitutive response; structurally and physically based models where a constitutive equation of a linear elastic material is modified by geometric characteristics. Viscoelasticity is incorporated into the existing constitutive models and the effect of hydration is discussed. We illustrate the importance of collagen with descriptions of its organization and properties in skin, fish scales, and bone, focusing on the findings of our group.

Mathematical and computational modeling in biology at multiple scales

A variety of topics are reviewed in the area of mathematical and computational modeling in biology, covering the range of scales from populations of organisms to electrons in atoms. The use of maximum entropy as an inference tool in the fields of biology and drug discovery is discussed. Mathematical and computational methods and models in the areas of epidemiology, cell physiology and cancer are surveyed. The technique of molecular dynamics is covered, with special attention to force fields for protein simulations and methods for the calculation of solvation free energies. The utility of quantum mechanical methods in biophysical and biochemical modeling is explored. The field of computational enzymology is examined.

Self-assembly of collagen on flat surfaces: the interplay of collagen-collagen and collagen-substrate interactions

Fibrillar collagens, common tissue scaffolds in live organisms, can also self-assemble in vitro from solution. While previous in vitro studies showed that the pH and the electrolyte concentration in solution largely control the collagen assembly, the physical reasons why such control could be exerted are still elusive. To address this issue and to be able to simulate self-assembly over large spatial and temporal scales, we have developed a microscopic model of collagen with explicit interactions between the units that make up the collagen molecules, as well as between these units and the substrate. We have used this model to investigate assemblies obtained via molecular dynamics deposition of collagen on a substrate at room temperature using an implicit solvent. By comparing the morphologies from our molecular dynamics simulations with those from our atomic-force microscopy experiments, we have found that the assembly is governed by the competition between the collagen-collagen interactions and those between collagen and the substrate. The microscopic model developed here can serve for guiding future experiments that would explore new regions of the parameter space.

Aggregation of lipid-anchored full-length H-Ras in lipid bilayers: simulations with the MARTINI force field

Lipid-anchored Ras oncoproteins assemble into transient, nano-sized substructures on the plasma membrane. These substructures, called nanoclusters, were proposed to be crucial for high-fidelity signal transmission in cells. However, the molecular basis of Ras nanoclustering is poorly understood. In this work, we used coarse-grained (CG) molecular dynamics simulations to investigate the molecular mechanism by which full-length H-ras proteins form nanoclusters in a model membrane. We chose two different conformations of H-ras that were proposed to represent the active and inactive state of the protein, and a domain-forming model bilayer made up of di16:0-PC (DPPC), di18:2-PC (DLiPC) and cholesterol. We found that, irrespective of the initial conformation, Ras molecules assembled into a single large aggregate. However, the two binding modes, which are characterized by the different orientation of the G-domain with respect to the membrane, differ in dynamics and organization during and after aggregation. Some of these differences involve regions of Ras that are important for effector/modulator binding, which may partly explain observed differences in the ability of active and inactive H-ras nanoclusters to recruit effectors. The simulations also revealed some limitations in the CG force field to study protein assembly in solution, which we discuss in the context of proposed potential avenues of improvement.