Structural transitions and energy landscape for Cowpea Chlorotic Mottle Virus capsid mechanics from nanomanipulation in vitro and in silico

The tubular cavity of tobacco mosaic virus shields mechanical stress and regulates disassembly

Here we probe Tobacco mosaic virus (TMV) particles immobilized on a solid surface under transversal mechanical stress. We use atomic force microscopy to implement punctual deformation with high force (∼nN) that induces immediate virus rupture (single indentation assay), and continuous cycles of low force (∼100 pN) that generate a gradual disassembly of the virus particle (mechanical fatigue assay). These experiments are interpreted with the help of TMV coarse-grained and finite elements simulations, which indicate that the tubular cavity screens the transmission of mechanical stress from the top to the bottom half of the virion structure. Likewise, mechanical fatigue experiments reveal how TMV disassembles following growing transversal rifts with different dynamics that depend on a combination of the applied force and the tubular geometry of the virus. Our results indicate how the cylindrical cavity of TMV cushions the lower half of the virus structure from mechanical stress and regulates mechanical disassembly. STATEMENT OF SIGNIFICANCE: The inability of plant viruses like tobacco mosaic virus (TMV) to infect mammals makes them ideal for technological applications. While TMV is known for it's durability, it's unclear if this is due solely to its capsid proteins or its tubular structure. Using Atomic Force Microscopy, coarse-grained and finite elements models, we found that the tubular hole screens the transmission of mechanical stress from the top to the bottom half of the virion structure. This characteristic induces a stepwise disassembly process from intact to half virus, finishing in the virion disruption. Since the energies between proteins are comparable to those of other viruses, there is a protective effect of the tubular cavity that transcends the size down to the nanoscale.

Structural Mechanisms of Forced Unfolding of Double-Stranded Fibrin Oligomers

Fibrin forms a polymeric scaffold of blood clots, which are subjected to deformation in their dynamic environment. The extensible fibrin network allows fibers to stretch without breaking, but the mechanisms of their forced elongation are not understood. We combined atomic force microscopy, computer simulations, and Machine Learning to explore the nanomechanics of double-stranded cross-linked fibrin oligomers (FO). From the experimental force-extension profiles, the median 63 pN unfolding force and median 8.1 nm peak-to-peak distance with corresponding 56 pN and 11.4 nm interquartile ranges indicate substantial scatter due to ∼3-5 nm extension fluctuation of the triple α-helical coiled-coils. From simulations, unraveling of FO is determined by coupled dissociation of the D:D interface, γ-nodules unfolding, and reversible unfolding-refolding of the coiled-coils. These can occur as single structural transitions (60% of the time) or mixed transitions (40% of the time), with an alternating order of strands in which unfolding transitions occur, i.e., if the previous transition takes place in one strand, the next transition occurs in the other strand. The double-stranded FO are less extensible but stiffer and more stable compared with the single-stranded oligomers. These findings provide important insights into the biomechanics and dynamic structural properties of fibrin necessary to understand the (sub)molecular origin of fibrin extensibility.

Virtual indentation of the empty capsid of the minute virus of mice using a minimal coarse-grained model

A minimal coarse-grained model for T=1 viral capsids assembled from 20 protein rigid trimers has been designed by extending a previously proposed form of the interaction energy written as a sum of anisotropic pairwise interactions between the trimeric capsomers. The extension of the model has been performed to properly account for the coupling between two internal coordinates: the one that measures the intercapsomer distance and the other that gives the intercapsomer dihedral angle. The model has been able to fit with less than a 10% error the atomic force microscopy (AFM) indentation experimental data for the empty capsid of the minute virus of mice (MVM), providing in this way an admissible picture of the main mechanisms behind the capsid deformations. In this scenario, the bending of the intercapsomer dihedral angle is the angular internal coordinate that can support larger deformations away from its equilibrium values, determining important features of the AFM indentation experiments as the elastic constants along the three symmetry axes of the capsid and the critical indentations. From the value of one of the parameters of our model, we conclude that trimers in the MVM must be quite oblate tops, in excellent agreement with their known structure. The transition from the linear to the nonlinear regimes sampled in the indentation process appears to be an interesting topic for future research in physical virology.

Surface Cross-Linking by Macromolecular Tethers Enhances Virus-like Particles' Resilience to Mucosal Stress Factors

Virus-like particles (VLPs) are emerging as nanoscaffolds in a variety of biomedical applications including delivery of vaccine antigens and cargo such as mRNA to mucosal surfaces. These soft, colloidal, and proteinaceous structures (capsids) are nevertheless susceptible to mucosal environmental stress factors. We cross-linked multiple capsid surface amino acid residues using homobifunctional polyethylene glycol tethers to improve the persistence and survival of the capsid to model mucosal stressors. Surface cross-linking enhanced the stability of VLPs assembled from Acinetobacter phage AP205 coat proteins in low pH (down to pH 4.0) and high protease concentration conditions (namely, in pig and mouse gastric fluids). Additionally, it increased the stiffness of VLPs under local mechanical indentation applied using an atomic force microscopy cantilever tip. Small angle X-ray scattering revealed an increase in capsid diameter after cross-linking and an increase in capsid shell thickness with the length of the PEG cross-linkers. Moreover, surface cross-linking had no effect on the VLPs' mucus translocation and accumulation on the epithelium of in vitro 3D human nasal epithelial tissues with mucociliary clearance. Finally, it did not compromise VLPs' function as vaccines in mouse subcutaneous vaccination models. Compared to PEGylation without cross-linking, the stiffness of surface cross-linked VLPs were higher for the same length of the PEG molecule, and also the lifetimes of surface cross-linked VLPs were longer in the gastric fluids. Surface cross-linking using macromolecular tethers, but not simple conjugation of these molecules, thus offers a viable means to enhance the resilience and survival of VLPs for mucosal applications.

Mechanical fatigue testing in silico: Dynamic evolution of material properties of nanoscale biological particles

Biological particles have evolved to possess mechanical characteristics necessary to carry out their functions. We developed a computational approach to "fatigue testing in silico", in which constant-amplitude cyclic loading is applied to a particle to explore its mechanobiology. We used this approach to describe dynamic evolution of nanomaterial properties and low-cycle fatigue in the thin spherical encapsulin shell, thick spherical Cowpea Chlorotic Mottle Virus (CCMV) capsid, and thick cylindrical microtubule (MT) fragment over 20 cycles of deformation. Changing structures and force-deformation curves enabled us to describe their damage-dependent biomechanics (strength, deformability, stiffness), thermodynamics (released and dissipated energies, enthalpy, and entropy) and material properties (toughness). Thick CCMV and MT particles experience material fatigue due to slow recovery and damage accumulation over 3-5 loading cycles; thin encapsulin shells show little fatigue due to rapid remodeling and limited damage. The results obtained challenge the existing paradigm: damage in biological particles is partially reversible owing to particle's partial recovery; fatigue crack may or may not grow with each loading cycle and may heal; and particles adapt to deformation amplitude and frequency to minimize the energy dissipated. Using crack size to quantitate damage is problematic as several cracks might form simultaneously in a particle. Dynamic evolution of strength, deformability, and stiffness, can be predicted by analyzing the cycle number (N) dependent damage, [Formula: see text] , where α is a power law and Nf is fatigue life. Fatigue testing in silico can now be used to explore damage-induced changes in the material properties of other biological particles. STATEMENT OF SIGNIFICANCE: Biological particles possess mechanical characteristics necessary to perform their functions. We developed "fatigue testing in silico" approach, which employes Langevin Dynamics simulations of constant-amplitude cyclic loading of nanoscale biological particles, to explore dynamic evolution of the mechanical, energetic, and material properties of the thin and thick spherical particles of encapsulin and Cowpea Chlorotic Mottle Virus, and the microtubule filament fragment. Our study of damage growth and fatigue development challenge the existing paradigm. Damage in biological particles is partially reversible as fatigue crack might heal with each loading cycle. Particles adapt to deformation amplitude and frequency to minimize energy dissipation. The evolution of strength, deformability, and stiffness, can be accurately predicted by analyzing the damage growth in particle structure.

Electromechanical Photophysics of GFP Packed Inside Viral Protein Cages Probed by Force-Fluorescence Hybrid Single-Molecule Microscopy

Packing biomolecules inside virus capsids has opened new avenues for the study of molecular function in confined environments. These systems not only mimic the highly crowded conditions in nature, but also allow their manipulation at the nanoscale for technological applications. Here, green fluorescent proteins are packed in virus-like particles derived from P22 bacteriophage procapsids. The authors explore individual virus cages to monitor their emission signal with total internal reflection fluorescence microscopy while simultaneously changing the microenvironment with the stylus of atomic force microscopy. The mechanical and electronic quenching can be decoupled by ≈10% each using insulator and conductive tips, respectively. While with conductive tips the fluorescence quenches and recovers regardless of the structural integrity of the capsid, with the insulator tips quenching only occurs if the green fluorescent proteins remain organized inside the capsid. The electronic quenching is associated with the coupling of the protein fluorescence emission with the tip surface plasmon resonance. In turn, the mechanical quenching is a consequence of the unfolding of the aggregated proteins during the mechanical disruption of the capsid.

Microtubule assembly and disassembly dynamics model: Exploring dynamic instability and identifying features of Microtubules' Growth, Catastrophe, Shortening, and Rescue

Microtubules (MTs), a cellular structure element, exhibit dynamic instability and can switch stochastically from growth to shortening; but the factors that trigger these processes at the molecular level are not understood. We developed a 3D Microtubule Assembly and Disassembly DYnamics (MADDY) model, based upon a bead-per-monomer representation of the αβ-tubulin dimers forming an MT lattice, stabilized by the lateral and longitudinal interactions between tubulin subunits. The model was parameterized against the experimental rates of MT growth and shortening, and pushing forces on the Dam1 protein complex due to protofilaments splaying out. Using the MADDY model, we carried out GPU-accelerated Langevin simulations to access dynamic instability behavior. By applying Machine Learning techniques, we identified the MT characteristics that distinguish simultaneously all four kinetic states: growth, catastrophe, shortening, and rescue. At the cellular 25 μM tubulin concentration, the most important quantities are the MT length L , average longitudinal curvatureκ long , MT tip width w , total energy of longitudinal interactions in MT latticeU long , and the energies of longitudinal and lateral interactions required to complete MT to full cylinderU long add andU lat add . At high 250 μM tubulin concentration, the most important characteristics are L ,κ long , number of hydrolyzed αβ-tubulin dimersn hyd and number of lateral interactions per helical pitchn lat in MT lattice, energy of lateral interactions in MT latticeU lat , and energy of longitudinal interactions in MT tipu long . These results allow greater insights into what brings about kinetic state stability and the transitions between states involved in MT dynamic instability behavior.

Strength, deformability and toughness of uncrosslinked fibrin fibers from theoretical reconstruction of stress-strain curves

Structural mechanisms underlying the mechanical properties of fibrin fibers are elusive. We combined tensile testing of uncrosslinked fibrin polymers in vitro and in silico to explore their material properties. The experimental stress (σ) - strain (ε) curves for fibrin fibers are characterized by elastic deformations with a weaker elastic response for ε<160% due to unraveling of αC tethers and straightening of fibrin protofibrils, and a stronger response for ε>160% owing to unfolding of the coiled coils and γ nodules in fibrin monomers. Fiber rupture for strains ε>212% is due to dissociation of the knob-hole bonds and rupture of D:D interfaces. We developed the Fluctuating Bilinear Spring model to interpret the σ-ε profiles in terms of the free energy for protofibril alignment ΔG0 = 10.1-11.5 kBT, Young's moduli for protofibril alignment Yu = 1.9-3.2 MPa and stretching Ya = 5.7-9.7 MPa, strain scale ε˜≈ 12-40% for fiber rupture, and protofibril cooperativity m= 3.6-8. We applied the model to characterize the fiber strength σcr≈ 12-13 MPa, deformability εcr≈ 222%, and rupture toughness U≈ 9 MJ/m3, and to resolve thermodynamic state functions, 96.9 GJ/mol entropy change for protofibril alignment (at room temperature) and 113.6 GJ/mol enthalpy change for protofibril stretching, which add up to 210.5 GJ/mol free-energy change. Fiber elongation is associated with protofibril dehydration and sliding mechanism to create an ordered protofibril array. Fibrin fibers behave like a hydrogel; protofibril dehydration and water expulsion account for ∼94-98% of the total free-energy changes for fiber elongation and rupture. STATEMENT OF SIGNIFICANCE: Structural mechanisms underlying the mechanical properties of fibrin fibers, major components of blood clots and obstructive thrombi, are elusive. We performed tensile testing of uncrosslinked fibrin polymers in vitro and in silico to explore their material properties. Fluctuating Bilinear Spring theory was developed to interpret the stress-strain profiles in terms of the energy for protofibril alignment, elastic moduli for protofibril alignment and stretching, and strain scale for fiber rupture, and to probe the limits of fiber strength, extensibility and toughness. Fibrin fibers behave like a hydrogel. Fiber elongation is defined by the protofibril dehydration and sliding. Structural rearrangements in water matrix control fiber elasticity. These results contribute to fundamental understanding of blood clot breakage that underlies thrombotic embolization.

Minimal Design Principles for Icosahedral Virus Capsids

The geometrical structures of single- and multiple-shell icosahedral virus capsids are reproduced as the targets that minimize the cost corresponding to relatively simple design functions. Capsid subunits are first identified as building blocks at a given coarse-grained scale and then represented in these functions as point particles located on an appropriate number of concentric spherical surfaces. Minimal design cost is assigned to optimal spherical packings of the particles. The cost functions are inspired by the packings favored for the Thomson problem, which minimize the electrostatic potential energy between identical charged particles. In some cases, icosahedral symmetry constraints are incorporated as external fields acting on the particles. The simplest cost functions can be obtained by separating particles in disjoint nonequivalent sets with distinct interactions, or by introducing interacting holes (the absence of particles). These functions can be adapted to reproduce any capsid structure found in real viruses. Structures absent in Nature require significantly more complex designs. Measures of information content and complexity are assigned to both the cost functions and the capsid geometries. In terms of these measures, icosahedral structures and the corresponding cost functions are the simplest solutions.

Modeling the Mechanical Response of Microtubule Lattices to Pressure

Microtubules, the largest and stiffest filaments of the cytoskeleton, have to be well adapted to the high levels of crowdedness in cells to perform their multitude of functions. Furthermore, fundamental processes that involve microtubules, such as the maintenance of the cellular shape and cellular motion, are known to be highly dependent on external pressure. In light of the importance of pressure for the functioning of microtubules, numerous studies interrogated the response of these cytoskeletal filaments to osmotic pressure, resulting from crowding by osmolytes, such as poly(ethylene glycol)/poly(ethylene oxide) (PEG/PEO) molecules, or to direct applied pressure. The interpretation of experiments is usually based on the assumptions that PEG molecules have unfavorable interactions with the microtubule lattices and that the behavior of microtubules under pressure can be described by using continuous models. We probed directly these two assumptions. First, we characterized the interaction between the main interfaces in a microtubule filament and PEG molecules of various sizes using a combination of docking and molecular dynamics simulations. Second, we studied the response of a microtubule filament to compression using a coarse-grained model that allows for the breaking of lattice interfaces. Our results show that medium length PEG molecules do not alter the energetics of the lateral interfaces in microtubules but rather target and can penetrate into the voids between tubulin monomers at these interfaces, which can lead to a rapid loss of lateral interfaces under pressure. Compression of a microtubule under conditions corresponding to high osmotic pressure results in the formation of the deformed phase found in experiments. Our simulations show that the breaking of lateral interfaces, rather than the buckling of the filament inferred from the continuous models, accounts for the deformation.

Fluctuating nonlinear spring theory: Strength, deformability, and toughness of biological nanoparticles from theoretical reconstruction of force-deformation spectra

We developed the Fluctuating Nonlinear Spring (FNS) model to describe the dynamics of mechanical deformation of biological particles, such as virus capsids. The theory interprets the force-deformation spectra in terms of the "Hertzian stiffness" (non-linear regime of a particle's small-amplitude deformations), elastic constant (large-amplitude elastic deformations), and force range in which the particle's fracture occurs. The FNS theory enables one to quantify the particles' elasticity (Young's moduli for Hertzian and bending deformations), and the limits of their strength (critical forces, fracture toughness) and deformability (critical deformations) as well as the probability distributions of these properties, and to calculate the free energy changes for the particle's Hertzian, elastic, and plastic deformations, and eventual fracture. We applied the FNS theory to describe the protein capsids of bacteriophage P22, Human Adenovirus, and Herpes Simplex virus characterized by deformations before fracture that did not exceed 10-19% of their size. These nanoshells are soft (~1-10-GPa elastic modulus), with low ~50-480-kPa toughness - a regime of material behavior that is not well understood, and with the strength increasing while toughness decreases with their size. The particles' fracture is stochastic, with the average values of critical forces, critical deformations, and fracture toughness comparable with their standard deviations. The FNS theory predicts 0.7-MJ/mol free energy for P22 capsid maturation, and it could be extended to describe uniaxial deformation of cylindrical microtubules and ellipsoidal cellular organelles.

Physics of viral dynamics

Viral capsids are often regarded as inert structural units, but in actuality they display fascinating dynamics during different stages of their life cycle. With the advent of single-particle approaches and high-resolution techniques, it is now possible to scrutinize viral dynamics during and after their assembly and during the subsequent development pathway into infectious viruses. In this Review, the focus is on the dynamical properties of viruses, the different physical virology techniques that are being used to study them, and the physical concepts that have been developed to describe viral dynamics.

Structural and dynamic asymmetry in icosahedrally symmetric virus capsids

A common characteristic of virus capsids is icosahedral symmetry, yet these highly symmetric structures can display asymmetric features within their virions and undergo asymmetric dynamics. The fields of structural and computational biology have entered a new realm in the investigation of virus infection mechanisms, with the ability to observe symmetry-breaking features. This review will cover important studies on icosahedral virus structure and dynamics, covering both symmetric and asymmetric conformational changes. However, the main emphasis of the review will be towards recent studies employing cryo-electron microscopy or molecular dynamics simulations, which can uncover asymmetric aspects of these systems relevant to understanding viral physical-chemical properties and their biological impact.

A minimal coarse-grained model for the low-frequency normal mode analysis of icosahedral viral capsids

The main goal of this work is the design of a coarse-grained theoretical model of minimal resolution for the study of the physical properties of icosahedral virus capsids within the linear-response regime. In this model the capsid is represented as an interacting many-body system whose composing elements are capsid subunits (capsomers), which are treated as three-dimensional rigid bodies. The total interaction potential energy is written as a sum of pairwise capsomer-capsomer interactions. Based on previous work [Gomez Llorente et al., Soft Matter, 2014, 10, 3560], a minimal and complete anisotropic binary interaction that includes a full Hessian matrix of independent force constants is proposed. In this interaction model, capsomers have rotational symmetry around an axis of order n > 2. The full coarse-grained model is applied to analyse the low-frequency normal-mode spectrum of icosahedral T = 1 capsids. The model performance is evaluated by fitting its predicted spectrum to the full-atom results for the Satellite Tobacco Necrosis Virus (STNV) capsid [Dykeman and Sankey, Phys. Rev. Lett., 2008, 100, 028101]. Two capsomer choices that are compatible with the capsid icosahedral symmetry are checked, namely pentamers (n = 5) and trimers (n = 3). Both subunit types provide fair fits, from which the magnitude of the coarse-grained force constants for a real virus is obtained. The model is able to uncover latent instabilities whose analysis is fully consistent with the current knowledge about the STNV capsid, which does not self-assemble in the absence of RNA and is thermally unstable. The straightforward generalisability of the model beyond the linear regime and its completeness make it a promising tool to theoretically interpret many experimental data such as those provided by the atomic force microscopy or even to better understand processes far from equilibrium such as the capsid self-assembly.

Kinetics of empty viral capsid assembly in a minimal model

The efficient construction of a protective protein shell or capsid is one of the most crucial steps in the replication cycle of a virus. The formation of the simplest capsid typically proceeds by the spontaneous assembly of identical building blocks. This process can also be achieved in vitro even in the absence of genetic material, thus opening the door to the production of artificial viral cages for a myriad of applications. In this work, we analyze the efficiency and the kinetic peculiarities of this self-assembly process using Brownian Dynamics simulations. We use a minimal model that considers identical assembly units and is able to reproduce successfully the correct final architecture of spherical capsids. The selection of a specific size and structure is achieved by changing a single parameter that imposes an angular anisotropy on the interaction. We analyze how the geometrical constraints of the interaction affect the efficiency of the assembly. We find that the optimal conditions for an efficient assembly from a kinetic point of view strongly depart from the lowest capsid energy corresponding to the minimum of the potential energy landscape. Our work illustrates the important differences between the equilibrium and dynamic characteristics of viral self-assembly, and provides important insights on how to design specific interactions for a successful assembly of artificial viral cages.

Future of cancer immunotherapy using plant virus-based nanoparticles

Immunotherapy potentiates a patient’s immune response against some forms of cancer, including malignant tumors. In this Special Report, we have summarized the use of nanoparticles that have been designed for use in cancer immunotherapy with particular emphasis on plant viruses. Plant virus-based nanoparticles are an ideal choice for therapeutic applications, as these nanoparticles are not only capable of targeting the desired cells but also of being safely delivered to the body without posing any threat of infection. Plant viruses can be taken up by tumor cells and can be functionalized as drug delivery vehicles. This Special Report describes how the future of cancer immunotherapy could be a success through the merger of computer-based technology using plant-virus nanoparticles.

The nonpathogenic nature of plant viral nanoparticles makes them an ideal choice for therapeutic applications such as cancer. Understanding the molecular mechanisms behind the immune response to cancer has facilitated the use of nanotechnology as an effective cancer therapy. Biologically active self-replicating plant virus particles can be introduced to the bloodstream of the human body and used as effective drug delivery vehicles. This Special Report describes how a combination of computer-based technology and plant-virus nanoparticles can assist in cancer immunotherapy.

Intermittency of Deformation and the Elastic Limit of an Icosahedral Virus under Compression

Viruses undergo mesoscopic morphological changes as they interact with host interfaces and in response to chemical cues. The dynamics of these changes, over the entire temporal range relevant to virus processes, are unclear. Here, we report on creep compliance experiments on a small icosahedral virus under uniaxial constant stress. We find that even at small stresses, well below the yielding point and generally thought to induce a Hookean response, strain continues to develop in time via sparse, randomly distributed, relatively rapid plastic events. The intermittent character of mechanical compliance only appears above a loading threshold, similar to situations encountered in granular flows and the plastic deformation of crystalline solids. The threshold load is much smaller for the empty capsids of the brome mosaic virus than for the wild-type virions. The difference highlights the involvement of RNA in stabilizing the assembly interface. Numerical simulations of spherical crystal deformation suggest intermittency is mediated by lattice defect dynamics and identify the type of compression-induced defect that nucleates the transition to plasticity.

Structural determinants of mechanical resistance against breakage of a virus-based protein nanoparticle at a resolution of single amino acids

Virus particles and other protein-based supramolecular complexes have a vast nanotechnological potential. However, protein nanostructures are "soft" materials prone to disruption by force. Whereas some non-biological nanoparticles (NPs) may be stronger, for certain applications protein- and virus-based NPs have potential advantages related to their structure, self-assembly, production, engineering, and/or inbuilt functions. Thus, it may be desirable to acquire the knowledge needed to engineer protein-based nanomaterials with a higher strength against mechanical breakage. Here we have used the capsid of the minute virus of mice to experimentally identify individual chemical groups that determine breakage-related properties of a virus particle. Individual amino acid side chains that establish interactions between building blocks in the viral particle were truncated using protein engineering. Indentation experiments using atomic force microscopy were carried out to investigate the role of each targeted side chain in determining capsid strength and brittleness, by comparing the maximum force and deformation each modified capsid withstood before breaking apart. Side chains with major roles in determining capsid strength against breakage included polar groups located in solvent-exposed positions, and did not generally correspond with those previously identified as determinants of mechanical stiffness. In contrast, apolar side chains buried along the intersubunit interfaces that generally determined capsid stiffness had, at most, a minor influence on strength against disruption. Whereas no correlated variations between strength and either stiffness or brittleness were found, brittleness and stiffness were quantitatively correlated. Implications for developing robust protein-based NPs and for acquiring a deeper physics-based perspective of viruses are discussed.

Viral nanomechanics with a virtual atomic force microscope

One of the most important components of a virus is the protein shell or capsid that encloses its genetic material. The main role of the capsid is to protect the viral genome against external aggressions, facilitating its safe and efficient encapsulation and delivery. As a consequence, viral capsids have developed astonishing mechanical properties that are crucial for viral function. These remarkable properties have started to be unveiled in single-virus nanoindentation experiments, and are opening the door to the use of viral-derived artificial nanocages for promising bio- and nano-technological applications. However, the interpretation of nanoindentation experiments is often difficult, requiring the support of theoretical and simulation analysis. Here we present a 'Virtual AFM' (VAFM), a Brownian Dynamics simulation of a coarse-grained model of virus aimed to mimic the standard setup of atomic force microscopy (AFM) nanoindentation experiments. Despite the heavy level of coarse-graining, these simulations provide valuable information which is not accessible in experiments. Rather than focusing on a specific virus, the VAFM will be used to analyze how the mechanical response and breaking of viruses depend on different parameters controlling the effective interactions between capsid's structural units. In particular, we will discuss the influence of adsorption, the tip radius, and the rigidity and shape of the shell on its mechanical response.

CapsidMesh: Atomic-detail structured mesh representation of icosahedral viral capsids and the study of their mechanical properties

Viruses are the most abundant pathogens affecting all forms of life. A major component of a virus is a protein shell, known as the viral capsid, that encapsulates the genomic material. The fundamental functions of the capsid are to protect and transport the viral genome and recognize the host cell. Descriptions of this macromolecular complex have been proposed at different scales of approximation. Here, we introduce a methodology to generate a structured volumetric mesh of icosahedral viral capsids (CapsidMesh) based on the atomic positions of their constituents. Material properties of the capsid proteins can be set on every mesh element individually. Hence, we have control over all levels of protein structure (atoms, amino acids, subunits, oligomers, and capsid). The CapsidMesh models are suitable for numerical simulations and analysis of a physical process using a third-party package. In particular, we used our methodology to generate a CapsidMesh of several capsids previously characterized by atomic force microscopy experiments and then simulated the mechanical nanoindentation through the finite element method. By fitting to the experimental linear elastic response, we estimated the elastic modulus and mechanical stresses produced on the capsids. Our results show that the atomic detail of the CapsidMesh is sufficient to reproduce anisotropic properties of the particle.

Membrane-containing virus particles exhibit the mechanics of a composite material for genome protection

The protection of the viral genome during extracellular transport is an absolute requirement for virus survival and replication. In addition to the almost universal proteinaceous capsids, certain viruses add a membrane layer that encloses their double-stranded (ds) DNA genome within the protein shell. Using the membrane-containing enterobacterial virus PRD1 as a prototype, and a combination of nanoindentation assays by atomic force microscopy and finite element modelling, we show that PRD1 provides a greater stability against mechanical stress than that achieved by the majority of dsDNA icosahedral viruses that lack a membrane. We propose that the combination of a stiff and brittle proteinaceous shell coupled with a soft and compliant membrane vesicle yields a tough composite nanomaterial well-suited to protect the viral DNA during extracellular transport.

Determination of prestress and elastic properties of virus capsids

Virus capsids are protein shells that protect the virus genome, and determination of their mechanical properties has been a topic of interest because of their potential use in nanotechnology and therapeutics. It has been demonstrated that stresses exist in virus capsids, even in their equilibrium state, due to their construction. These stresses, termed "prestresses" in this study, closely affect the capsid's mechanical behavior. Three methods-shape-based metric, atomic force microscope indentation, and molecular dynamics-have been proposed to determine the capsid elastic properties without fully accounting for prestresses. In this paper, we theoretically analyze the three methods used for mechanical characterization of virus capsids and numerically investigate how prestresses affect the capsid's mechanical properties. We consolidate all the results and propose that by using these techniques collectively, it is possible to accurately determine both the mechanical properties and prestresses in capsids.

TensorCalculator: exploring the evolution of mechanical stress in the CCMV capsid

A new computational methodology for the accurate numerical calculation of the Cauchy stress tensor, stress invariants, principal stress components, von Mises and Tresca tensors is developed. The methodology is based on the atomic stress approach which permits the calculation of stress tensors, widely used in continuum mechanics modeling of materials properties, using the output from the MD simulations of discrete atomic and [Formula: see text]-based coarse-grained structural models of biological particles. The methodology mapped into the software package TensorCalculator was successfully applied to the empty cowpea chlorotic mottle virus (CCMV) shell to explore the evolution of mechanical stress in this mechanically-tested specific example of a soft virus capsid. We found an inhomogeneous stress distribution in various portions of the CCMV structure and stress transfer from one portion of the virus structure to another, which also points to the importance of entropic effects, often ignored in finite element analysis and elastic network modeling. We formulate a criterion for elastic deformation using the first principal stress components. Furthermore, we show that von Mises and Tresca stress tensors can be used to predict the onset of a viral capsid's mechanical failure, which leads to total structural collapse. TensorCalculator can be used to study stress evolution and dynamics of defects in viral capsids and other large-size protein assemblies.

Mechanical stiffening of human rhinovirus by cavity-filling antiviral drugs

Emerging studies at the nanoscale on the relationships between the structure, mechanical properties and infectivity of virus particles are revealing important physics-based foundations of virus biology that may have biomedical and nanotechnological applications. Human rhinovirus (HRV) is the major causative agent of common colds leading to important economic losses, and is also associated with more severe diseases. There is renewed interest in developing effective anti-HRV drugs, but none have been approved so far. We have chosen HRV to explore a possible link between virus mechanics and infectivity and the antiviral effect of certain drugs. In particular, we have investigated a suggestion that the antiviral action of drugs that bind to capsid cavities (pockets) may be related to changes in virus stiffness. Mechanical analysis using atomic force microscopy shows that filling the pockets with drugs or genetically introducing bulkier amino acid side chains into the pockets stiffen HRV virions to different extents. Drug-mediated stiffening affected some regions distant from the pockets and involved in genome uncoating, and may be caused by a subtle structural rearrangement of the virus particle. The results also revealed for HRV a quantitative, logarithmic relationship between mechanical stiffening, achieved either by drug binding or introducing bulkier amino acid side chains into the pockets, and reduced infectivity. From a fundamental physics perspective, these drugs may exert their biological effect by decreasing the deformability of the virion, thus impairing its equilibrium dynamics. The results encourage the design of novel antiviral drugs that inhibit infection by mechanically stiffening the viral particles.

Self-assembly of model proteins into virus capsids

We consider self-assembly of proteins into a virus capsid by the methods of molecular dynamics. The capsid corresponds either to SPMV or CCMV and is studied with and without the RNA molecule inside. The proteins are flexible and described by the structure-based coarse-grained model augmented by electrostatic interactions. Previous studies of the capsid self-assembly involved solid objects of a supramolecular scale, e.g. corresponding to capsomeres, with engineered couplings and stochastic movements. In our approach, a single capsid is dissociated by an application of a high temperature for a variable period and then the system is cooled down to allow for self-assembly. The restoration of the capsid proceeds to various extent, depending on the nature of the dissociated state, but is rarely complete because some proteins depart too far unless the process takes place in a confined space.

Modeling the effects of lattice defects on microtubule breaking and healing

Microtubule reorganization often results from the loss of polymer induced through breakage or active destruction by energy-using enzymes. Pre-existing defects in the microtubule lattice likely lower structural integrity and aid filament destruction. Using large-scale molecular simulations, we model diverse microtubule fragments under forces generated at specific positions to locally crush the filament. We show that lattices with 2% defects are crushed and severed by forces three times smaller than defect-free ones. We validate our results with direct comparisons of microtubule kinking angles during severing. We find a high statistical correlation between the angle distributions from experiments and simulations indicating that they sample the same population of structures. Our simulations also indicate that the mechanical environment of the filament affects breaking: local mechanical support inhibits healing after severing, especially in the case of filaments with defects. These results recall reports of microtubule healing after flow-induced bending and corroborate prior experimental studies that show severing is more likely at locations where microtubules crossover in networks. Our results shed new light on mechanisms underlying the ability of microtubules to be destroyed and healed in the cell, either by external forces or by severing enzymes wedging dimers apart. © 2016 Wiley Periodicals, Inc.

AFM nanoindentation of protein shells, expanding the approach beyond viruses

The archetypical protein nanoshell is the capsid that surrounds viral genomes. These capsids protect the viral RNA or DNA and function as transport vehicle for their nucleic acid. The material properties of a variety of viral capsids have been probed by Atomic Force Microscopy. In particular nanoindentation measurements revealed the complex mechanics of these shells and the intricate interplay of the capsid with its genomic content. Furthermore, effects of capsid protein mutations, capsid maturation and the effect of environmental changes have been probed. In addition, biological questions have been addressed by AFM nanoindentation of viruses and a direct link between mechanics and infectivity has been revealed. Recently, non-viral protein nanoshells have come under intense scrutiny and now the nanoindentation approach has been expanded to such particles as well. Both natural as well as engineered non-viral protein shells have been probed by this technique. Next to the material properties of viruses, therefor also the mechanics of encapsulins, carboxysomes, vault particles, lumazine synthase and artificial protein nanoshells is discussed here.

Structural basis for biologically relevant mechanical stiffening of a virus capsid by cavity-creating or spacefilling mutations

Recent studies reveal that the mechanical properties of virus particles may have been shaped by evolution to facilitate virus survival. Manipulation of the mechanical behavior of virus capsids is leading to a better understanding of viral infection, and to the development of virus-based nanoparticles with improved mechanical properties for nanotechnological applications. In the minute virus of mice (MVM), deleterious mutations around capsid pores involved in infection-related translocation events invariably increased local mechanical stiffness and interfered with pore-associated dynamics. To provide atomic-resolution insights into biologically relevant changes in virus capsid mechanics, we have determined by X-ray crystallography the structural effects of deleterious, mechanically stiffening mutations around the capsid pores. Data show that the cavity-creating N170A mutation at the pore wall does not induce any dramatic structural change around the pores, but instead generates subtle rearrangements that propagate throughout the capsid, resulting in a more compact, less flexible structure. Analysis of the spacefilling L172W mutation revealed the same relationship between increased stiffness and compacted capsid structure. Implications for understanding connections between virus mechanics, structure, dynamics and infectivity, and for engineering modified virus-based nanoparticles, are discussed.

Vertex-Specific Proteins pUL17 and pUL25 Mechanically Reinforce Herpes Simplex Virus Capsids

Using atomic force microscopy imaging and nanoindentation measurements, we investigated the effect of the minor capsid proteins pUL17 and pUL25 on the structural stability of icosahedral herpes simplex virus capsids. pUL17 and pUL25, which form the capsid vertex-specific component (CVSC), particularly contributed to capsid resilience along the 5-fold and 2-fold but not along the 3-fold icosahedral axes. Our detailed analyses, including quantitative mass spectrometry of the protein composition of the capsids, revealed that both pUL17 and pUL25 are required to stabilize the capsid shells at the vertices. This indicates that herpesviruses withstand the internal pressure that is generated during DNA genome packaging by locally reinforcing the mechanical sturdiness of the vertices, the most stressed part of the capsids.IMPORTANCE In this study, the structural, material properties of herpes simplex virus 1 were investigated. The capsid of herpes simplex virus is built up of a variety of proteins, and we scrutinized the influence of two of these proteins on the stability of the capsid. For this, we used a scanning force microscope that makes detailed, topographic images of the particles and that is able to perform mechanical deformation measurements. Using this approach, we revealed that both studied proteins play an essential role in viral stability. These new insights support us in forming a complete view on viral structure and furthermore could possibly help not only to develop specific antivirals but also to build protein shells with improved stability for drug delivery purposes.

Mechanistic Basis for the Binding of RGD- and AGDV-Peptides to the Platelet Integrin αIIbβ3

Binding of soluble fibrinogen to the activated conformation of the integrin αIIbβ3 is required for platelet aggregation and is mediated exclusively by the C-terminal AGDV-containing dodecapeptide (γC-12) sequence of the fibrinogen γ chain. However, peptides containing the Arg-Gly-Asp (RGD) sequences located in two places in the fibrinogen Aα chain inhibit soluble fibrinogen binding to αIIbβ3 and make substantial contributions to αIIbβ3 binding when fibrinogen is immobilized and when it is converted to fibrin. Here, we employed optical trap-based nanomechanical measurements and computational molecular modeling to determine the kinetics, energetics, and structural details of cyclic RGDFK (cRGDFK) and γC-12 binding to αIIbβ3. Docking analysis revealed that NMR-determined solution structures of cRGDFK and γC-12 bind to both the open and closed αIIbβ3 conformers at the interface between the αIIb β-propeller domain and the β3 βI domain. The nanomechanical measurements revealed that cRGDFK binds to αIIbβ3 at least as tightly as γC-12. A subsequent analysis of molecular force profiles and the number of peptide-αIIbβ3 binding contacts revealed that both peptides form stable bimolecular complexes with αIIbβ3 that dissociate in the 60-120 pN range. The Gibbs free energy profiles of the αIIbβ3-peptide complexes revealed that the overall stability of the αIIbβ3-cRGDFK complex was comparable with that of the αIIbβ3-γC-12 complex. Thus, these results provide a mechanistic explanation for previous observations that RGD- and AGDV-containing peptides are both potent inhibitors of the αIIbβ3-fibrinogen interactions and are consistent with the observation that RGD motifs, in addition to AGDV, support interaction of αIIbβ3 with immobilized fibrinogen and fibrin.

Amino Acid Side Chains Buried along Intersubunit Interfaces in a Viral Capsid Preserve Low Mechanical Stiffness Associated with Virus Infectivity

Single-molecule experimental techniques and theoretical approaches reveal that important aspects of virus biology can be understood in biomechanical terms at the nanoscale. A detailed knowledge of the relationship in virus capsids between small structural changes caused by single-point mutations and changes in mechanical properties may provide further physics-based insights into virus function; it may also facilitate the engineering of viral nanoparticles with improved mechanical behavior. Here, we used the minute virus of mice to undertake a systematic experimental study on the contribution to capsid stiffness of amino acid side chains at interprotein interfaces and the specific noncovalent interactions they establish. Selected side chains were individually truncated by introducing point mutations to alanine, and the effects on local and global capsid stiffness were determined using atomic force microscopy. The results revealed that, in the natural virus capsid, multiple, mostly hydrophobic, side chains buried along the interfaces between subunits preserve a comparatively low stiffness of most (S2 and S3) regions. Virtually no point mutation tested substantially reduced stiffness, whereas most mutations increased stiffness of the S2/S3 regions. This stiffening was invariably associated with reduced virus yields during cell infection. The experimental evidence suggests that a comparatively low stiffness at S3/S2 capsid regions may have been biologically selected because it facilitates capsid assembly, increasing infectious virus yields. This study demonstrated also that knowledge of individual amino acid side chains and biological pressures that determine the physical behavior of a protein nanoparticle may be used for engineering its mechanical properties.

SOP-GPU: influence of solvent-induced hydrodynamic interactions on dynamic structural transitions in protein assemblies

Hydrodynamic interactions (HI) are incorporated into Langevin dynamics of the Cα -based protein model using the Truncated Expansion approximation (TEA) to the Rotne-Prager-Yamakawa diffusion tensor. Computational performance of the obtained GPU realization demonstrates the model's capability for describing protein systems of varying complexity (10(2) -10(5) residues), including biological particles (filaments, virus shells). Comparison of numerical accuracy of the TEA versus exact description of HI reveals similar results for the kinetics and thermodynamics of protein unfolding. The HI speed up and couple biomolecular transitions through cross-communication among protein domains, which result in more collective displacements of structure elements governed by more deterministic (less variable) dynamics. The force-extension/deformation spectra from nanomanipulations in silico exhibit sharper force signals that match well the experimental profiles. Hence, biomolecular simulations without HI overestimate the role of tension/stress fluctuations. Our findings establish the importance of incorporating implicit water-mediated many-body effects into theoretical modeling of dynamic processes involving biomolecules. © 2016 Wiley Periodicals, Inc.

Swelling and softening of the cowpea chlorotic mottle virus in response to pH shifts

Cowpea chlorotic mottle virus (CCMV) forms highly elastic icosahedral protein capsids that undergo a characteristic swelling transition when the pH is raised from 5 to 7. Here, we performed nano-indentation experiments using an atomic force microscope to track capsid swelling and measure the shells' Young's modulus at the same time. When we chelated Ca(2+) ions and raised the pH, we observed a gradual swelling of the RNA-filled capsids accompanied by a softening of the shell. Control experiments with empty wild-type virus and a salt-stable mutant revealed that the softening was not strictly coupled to the swelling of the protein shells. Our data suggest that a pH increase and Ca(2+) chelation lead primarily to a loosening of contacts within the protein shell, resulting in a softening of the capsid. This appears to render the shell metastable and make swelling possible when repulsive forces among the capsid proteins become large enough, which is known to be followed by capsid disassembly at even higher pH. Thus, softening and swelling are likely to play a role during inoculation.

Fluctuating Nonlinear Spring Model of Mechanical Deformation of Biological Particles

The mechanical properties of virus capsids correlate with local conformational dynamics in the capsid structure. They also reflect the required stability needed to withstand high internal pressures generated upon genome loading and contribute to the success of important events in viral infectivity, such as capsid maturation, genome uncoating and receptor binding. The mechanical properties of biological nanoparticles are often determined from monitoring their dynamic deformations in Atomic Force Microscopy nanoindentation experiments; but a comprehensive theory describing the full range of observed deformation behaviors has not previously been described. We present a new theory for modeling dynamic deformations of biological nanoparticles, which considers the non-linear Hertzian deformation, resulting from an indenter-particle physical contact, and the bending of curved elements (beams) modeling the particle structure. The beams’ deformation beyond the critical point triggers a dynamic transition of the particle to the collapsed state. This extreme event is accompanied by a catastrophic force drop as observed in the experimental or simulated force (F)-deformation (X) spectra. The theory interprets fine features of the spectra, including the nonlinear components of the FX-curves, in terms of the Young’s moduli for Hertzian and bending deformations, and the structural damage dependent beams’ survival probability, in terms of the maximum strength and the cooperativity parameter. The theory is exemplified by successfully describing the deformation dynamics of natural nanoparticles through comparing theoretical curves with experimental force-deformation spectra for several virus particles. This approach provides a comprehensive description of the dynamic structural transitions in biological and artificial nanoparticles, which is essential for their optimal use in nanotechnology and nanomedicine applications.

Dynamic force experiments, which have become available to explore the physical properties of biological assemblies, oftentimes reveal results that are difficult to understand without theoretical framework. We employed a multiscale modeling approach—a combination of Molecular Dynamics simulations of atomic structures with Langevin simulations of coarse-grained models of virus shells—to characterize the degrees of freedom defining the deformation and structural collapse of biological particles tested mechanically. This enabled us to develop an analytical model that provides meaningful interpretation of force-deformation spectra available from single-particle nanoindentation experiments. The Fluctuating Nonlinear Spring (FNS) model of uniaxial particle’s deformation captures essential features of the force-deformation spectra as observed in nanomanipulations in vitro and in silico: initial non-linearity, then a subsequent force decrease transition due to structural collapse. Our theory uniquely combines the elements of continuum mechanics with the statistics of extremes, enabling one to gather mechanical and statistical characteristics of nanoparticles, which determine the Hertzian deformation of the particle’s protein layer, and bending deformation and structural damage to the particle structure. We have demonstrated how the FNS theory can accurately model the deformation of several viral shells, showing promising model applications for describing a variety of natural and synthetic nanoparticles.

Nonuniform elastic properties of macromolecules and effect of prestrain on their continuum nature

Many experimental and theoretical methods have been developed to calculate the coarse-grained continuum elastic properties of macromolecules. However, all of those methods assume uniform elastic properties. Following the continuum mechanics framework, we present a systematic way of calculating the nonuniform effective elastic properties from atomic thermal fluctuations obtained from molecular dynamics simulation at any coarse-grained scale using a potential of the mean-force approach. We present the results for a mutant of Sesbania mosaic virus capsid, where we calculate the elastic moduli at different scales and observe an apparent problem with the chosen reference configuration in some cases. We present a possible explanation using an elastic network model, where inducing random prestrain results in a similar behavior. This phenomenon provides a novel insight into the continuum nature of macromolecules and defines the limits on details that the elasticity theory can capture. Further investigation into prestrains could elucidate important aspects of conformational dynamics of macromolecules.

Nucleotides regulate the mechanical hierarchy between subdomains of the nucleotide binding domain of the Hsp70 chaperone DnaK

The regulation of protein function through ligand-induced conformational changes is crucial for many signal transduction processes. The binding of a ligand alters the delicate energy balance within the protein structure, eventually leading to such conformational changes. In this study, we elucidate the energetic and mechanical changes within the subdomains of the nucleotide binding domain (NBD) of the heat shock protein of 70 kDa (Hsp70) chaperone DnaK upon nucleotide binding. In an integrated approach using single molecule optical tweezer experiments, loop insertions, and steered coarse-grained molecular simulations, we find that the C-terminal helix of the NBD is the major determinant of mechanical stability, acting as a glue between the two lobes. After helix unraveling, the relative stability of the two separated lobes is regulated by ATP/ADP binding. We find that the nucleotide stays strongly bound to lobe II, thus reversing the mechanical hierarchy between the two lobes. Our results offer general insights into the nucleotide-induced signal transduction within members of the actin/sugar kinase superfamily.

Stability of Norwalk Virus Capsid Protein Interfaces Evaluated by in Silico Nanoindentation

Norwalk virus causes severe gastroenteritis for which there is currently no specific anti-viral therapy. A stage of the infection process is uncoating of the protein capsid to expose the viral genome and allow for viral replication. A mechanical characterization of the Norwalk virus may provide important information relating to the mechanism of uncoating. The mechanical strength of the Norwalk virus has previously been investigated using atomic force microscopy (AFM) nanoindentation experiments. Those experiments cannot resolve specific molecular interactions, and therefore, we have employed a molecular modeling approach to gain insights into the potential uncoating mechanism of the Norwalk capsid. In this study, we perform simulated nanoindentation using a coarse-grained structure-based model, which provides an estimate of the spring constant in good agreement with the experimentally determined value. We further analyze the fracture mechanisms and determine weak interfaces in the capsid structure, which are potential sites to inhibit uncoating by stabilization of these weak interfaces. We conclude by identifying potential target sites at the junction of a weak protein–protein interface.

Tubulin bond energies and microtubule biomechanics determined from nanoindentation in silico

Microtubules, the primary components of the chromosome segregation machinery, are stabilized by longitudinal and lateral noncovalent bonds between the tubulin subunits. However, the thermodynamics of these bonds and the microtubule physicochemical properties are poorly understood. Here, we explore the biomechanics of microtubule polymers using multiscale computational modeling and nanoindentations in silico of a contiguous microtubule fragment. A close match between the simulated and experimental force–deformation spectra enabled us to correlate the microtubule biomechanics with dynamic structural transitions at the nanoscale. Our mechanical testing revealed that the compressed MT behaves as a system of rigid elements interconnected through a network of lateral and longitudinal elastic bonds. The initial regime of continuous elastic deformation of the microtubule is followed by the transition regime, during which the microtubule lattice undergoes discrete structural changes, which include first the reversible dissociation of lateral bonds followed by irreversible dissociation of the longitudinal bonds. We have determined the free energies of dissociation of the lateral (6.9 ± 0.4 kcal/mol) and longitudinal (14.9 ± 1.5 kcal/mol) tubulin–tubulin bonds. These values in conjunction with the large flexural rigidity of tubulin protofilaments obtained (18,000–26,000 pN·nm²) support the idea that the disassembling microtubule is capable of generating a large mechanical force to move chromosomes during cell division. Our computational modeling offers a comprehensive quantitative platform to link molecular tubulin characteristics with the physiological behavior of microtubules. The developed in silico nanoindentation method provides a powerful tool for the exploration of biomechanical properties of other cytoskeletal and multiprotein assemblies.

Recent Developments in Molecular Simulation Approaches to Study Spherical Virus Capsids

Viruses are a particularly challenging systems to study via molecular simulation methods. Virus capsids typically consist of over 100 subunit proteins and reach dimensions of over 100 nm; solvated viruses capsid systems can be over 1 million atoms in size. In this review, I will present recent developments which have attempted to overcome the significant computational expense to perform simulations which can inform experimental studies, make useful predictions about biological phenomena and calculate material properties relevant to nanotechnology design efforts.