Charge transport in individual short base stacked single-stranded RNA molecules.

Charge transport in biomolecules is crucial for many biological and technological applications, including biomolecular electronics devices and biosensors. RNA has become the focus of research because of its importance in biomedicine, but its charge transport properties are not well understood. Here, we use the Scanning Tunneling Microscopy-assisted molecular break junction method to measure the electrical conductance of particular 5-base and 10-base single-stranded (ss) RNA sequences capable of base stacking. These ssRNA sequences show single-molecule conductance values around [Formula: see text] ([Formula: see text]), while equivalent-length ssDNAs result in featureless conductance histograms. Circular dichroism (CD) spectra and MD simulations reveal the existence of extended ssRNA conformations versus folded ssDNA conformations, consistent with their different electrical behaviors. Computational molecular modeling and Machine Learning-assisted interpretation of CD data helped us to disentangle the structural and electronic factors underlying CT, thus explaining the observed electrical behavior differences. RNA with a measurable conductance corresponds to sequences with overall extended base-stacking stabilized conformations characterized by lower HOMO energy levels delocalized over a base-stacking mediating CT pathway. In contrast, DNA and a control RNA sequence without significant base-stacking tend to form closed structures and thus are incapable of efficient CT.

Biomechanics, Energetics, and Structural Basis of Rupture of Fibrin Networks.

Fibrin provides the main structural integrity and mechanical strength to blood clots. Failure of fibrin clots can result in life-threating complications, such as stroke or pulmonary embolism. The dependence of rupture resistance of fibrin networks (uncracked and cracked) on fibrin(ogen) concentrations in the (patho)physiological 1-5 g L-1 range is explored by performing the ultrastructural studies and theoretical analysis of the experimental stress-strain profiles available from mechanical tensile loading assays. Fibrin fibers in the uncracked network stretched evenly, whereas, in the cracked network, fibers around the crack tip showed greater deformation. Unlike fibrin fibers in cracked networks formed at the lower 1-2.7 g L-1 fibrinogen concentrations, fibers formed at the higher 2.7-5 g L-1 concentrations align and stretch simultaneously. Cracked fibrin networks formed in higher fibrinogen solutions are tougher yet less extensible. Statistical modeling revealed that the characteristic strain for fiber alignment, crack size, and fracture toughness of fibrin networks control their rupture resistance. The results obtained provide a structural and biomechanical basis to quantitatively understand the material properties of blood plasma clots and to illuminate the mechanisms of their rupture.

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.

Therapeutic phosphorodiamidate morpholino oligonucleotides: Physical properties, solution structures, and folding thermodynamics.

Elucidating the structure-function relationships for therapeutic RNA mimicking phosphorodiamidate morpholino oligonucleotides (PMOs) is challenging due to the lack of information about their structures. While PMOs have been approved by the US Food and Drug Administration for treatment of Duchenne muscular dystrophy, no structural information on these unique, charge-neutral, and stable molecules is available. We performed circular dichroism and solution viscosity measurements combined with molecular dynamics simulations and machine learning to resolve solution structures of 22-mer, 25-mer, and 30-mer length PMOs. The PMO conformational dynamics are defined by the competition between non-polar nucleobases and uncharged phosphorodiamidate groups for shielding from solvent exposure. PMO molecules form non-canonical, partially helical, stable folded structures with a small 1.4- to 1.7-nm radius of gyration, low count of three to six base pairs and six to nine base stacks, characterized by -34 to -51 kcal/mol free energy, -57 to -103 kcal/mol enthalpy, and -23 to -53 kcal/mol entropy for folding. The 4.5- to 6.2-cm3/g intrinsic viscosity and Huggins constant of 4.5-9.9 are indicative of extended and aggregating systems. The results obtained highlight the importance of the conformational ensemble view of PMO solution structures, thermodynamic stability of their non-canonical structures, and concentration-dependent viscosity properties. These principles form a paradigm to understand the structure-properties-function relationship for therapeutic PMOs to advance the design of new RNA-mimic-based drugs.

Interrelated effects of chromosome size, mechanics, number, location-orientation and polar ejection force on the spindle accuracy: a 3D computational study.

The search-and-capture model of spindle assembly has been a guiding principle for understanding prometaphase for decades. The computational model presented allows one to address two questions: how rapidly the microtubule-kinetochore connections are made, and how accurate these connections are. In most previous numerical simulations, the model geometry was drastically simplified. Using the CellDynaMo computational platform, we previously introduced a geometrically and mechanically realistic 3D model of the prometaphase mitotic spindle, and used it to evaluate thermal noise and microtubule kinetics effects on the capture of a single chromosome. Here, we systematically investigate how geometry and mechanics affect a spindle assembly's speed and accuracy, including nuanced distinctions between merotelic, mero-amphitelic, and mero-syntelic chromosomes. We find that softening of the centromere spring improves accuracy for short chromosome arms, but accuracy disappears for long chromosome arms. Initial proximity of chromosomes to one spindle pole makes assembly accuracy worse, while initial chromosome orientation matters less. Chromokinesins, added onto flexible chromosome arms, allow modeling of the polar ejection force, improving a spindle assembly's accuracy for a single chromosome. However, spindle space crowding by multiple chromosomes worsens assembly accuracy. Our simulations suggest that the complex microtubule network of the early spindle is key to rapid and accurate assembly.

CellDynaMo-stochastic reaction-diffusion-dynamics model: Application to search-and-capture process of mitotic spindle assembly.

We introduce a Stochastic Reaction-Diffusion-Dynamics Model (SRDDM) for simulations of cellular mechanochemical processes with high spatial and temporal resolution. The SRDDM is mapped into the CellDynaMo package, which couples the spatially inhomogeneous reaction-diffusion master equation to account for biochemical reactions and molecular transport within the Langevin Dynamics (LD) framework to describe dynamic mechanical processes. This computational infrastructure allows the simulation of hours of molecular machine dynamics in reasonable wall-clock time. We apply SRDDM to test performance of the Search-and-Capture of mitotic spindle assembly by simulating, in three spatial dimensions, dynamic instability of elastic microtubules anchored in two centrosomes, movement and deformations of geometrically realistic centromeres with flexible kinetochores and chromosome arms. Furthermore, the SRDDM describes the mechanics and kinetics of Ndc80 linkers mediating transient attachments of microtubules to the chromosomal kinetochores. The rates of these attachments and detachments depend upon phosphorylation states of the Ndc80 linkers, which are regulated in the model by explicitly accounting for the reactions of Aurora A and B kinase enzymes undergoing restricted diffusion. We find that there is an optimal rate of microtubule-kinetochore detachments which maximizes the accuracy of the chromosome connections, that adding chromosome arms to kinetochores improve the accuracy by slowing down chromosome movements, that Aurora A and kinetochore deformations have a small positive effect on the attachment accuracy, and that thermal fluctuations of the microtubules increase the rates of kinetochore capture and also improve the accuracy of spindle assembly.

Fibrin protofibril packing and clot stability are enhanced by extended knob-hole interactions and catch-slip bonds.

Fibrin polymerization involves thrombin-mediated exposure of knobs on one monomer that bind to holes available on another, leading to the formation of fibers. In silico evidence has suggested that the classical A:a knob-hole interaction is enhanced by surrounding residues not directly involved in the binding pocket of hole a, via noncovalent interactions with knob A. We assessed the importance of extended knob-hole interactions by performing biochemical, biophysical, and in silico modeling studies on recombinant human fibrinogen variants with mutations at residues responsible for the extended interactions. Three single fibrinogen variants, γD297N, γE323Q, and γK356Q, and a triple variant γDEK (γD297N/γE323Q/γK356Q) were produced in a CHO (Chinese Hamster Ovary) cell expression system. Longitudinal protofibril growth probed by atomic force microscopy was disrupted for γD297N and enhanced for the γK356Q mutation. Initial polymerization rates were reduced for all variants in turbidimetric studies. Laser scanning confocal microscopy showed that γDEK and γE323Q produced denser clots, whereas γD297N and γK356Q were similar to wild type. Scanning electron microscopy and light scattering studies showed that fiber thickness and protofibril packing of the fibers were reduced for all variants. Clot viscoelastic analysis showed that only γDEK was more readily deformable. In silico modeling suggested that most variants displayed only slip-bond dissociation kinetics compared with biphasic catch-slip kinetics characteristics of wild type. These data provide new evidence for the role of extended interactions in supporting the classical knob-hole bonds involving catch-slip behavior in fibrin formation, clot structure, and clot mechanics.

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 αß-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 curvature κ long , MT tip width w , total energy of longitudinal interactions in MT lattice U long , and the energies of longitudinal and lateral interactions required to complete MT to full cylinder U long add and U lat add . At high 250 µM tubulin concentration, the most important characteristics are L , κ long , number of hydrolyzed αß-tubulin dimers n hyd and number of lateral interactions per helical pitch n lat in MT lattice, energy of lateral interactions in MT lattice U lat , and energy of longitudinal interactions in MT tip u long . These results allow greater insights into what brings about kinetic state stability and the transitions between states involved in MT dynamic instability behavior.

Single-molecule conductance of double-stranded RNA oligonucleotides.

RNA oligonucleotides are crucial for a range of biological functions and in many biotechnological applications. Herein, we measured, for the first time, the conductance of individual double-stranded (ds)RNA molecules and compared it with the conductance of single DNA : RNA hybrids. The average conductance values are similar for both biomolecules, but the distribution of conductance values shows an order of magnitude higher variability for dsRNA, indicating higher molecular flexibility of dsRNA. Microsecond Molecular Dynamics simulations explain this difference and provide structural insights into the higher stability of DNA : RNA duplex with atomic level of detail. The rotations of 2'-OH groups of the ribose rings and the bases in RNA strands destabilize the duplex structure by weakening base stacking interactions, affecting charge transport, and making single-molecule conductance of dsRNA more variable (dynamic disorder). The results demonstrate that a powerful combination of state-of-the-art biomolecular electronics techniques and computational approaches can provide valuable insights into biomolecules' biophysics with unprecedented spatial resolution.

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.

Strength and deformability of fibrin clots: Biomechanics, thermodynamics, and mechanisms of rupture.

Fibrin is the major determinant of the mechanical stability and integrity of blood clots and thrombi. To explore the rupture of blood clots, emulating thrombus breakage, we stretched fibrin gels with single-edge cracks of varying size. Ultrastructural alterations of the fibrin network correlated with three regimes of stress vs. strain profiles: the weakly non-linear regime due to alignment of fibrin fibers; linear regime owing to further alignment and stretching of fibers; and the rupture regime for large deformations reaching the critical strain and stress, at which irreversible breakage of fibers ahead of the crack tip occurs. To interpret the stress-strain curves, we developed a new Fluctuating Spring model, which maps the fibrin alignment at the characteristic strain, network stretching with the Young modulus, and simultaneous cooperative rupture of coupled fibrin fibers into a theoretical framework to obtain the closed-form expressions for the strain-dependent stress profiles. Cracks render network rupture stochastic, and the free energy change for fiber deformation and rupture decreases with the crack length, making network rupture more spontaneous. By contrast, mechanical cooperativity due to the presence of inter-fiber contacts strengthens fibrin networks. The results obtained provide a fundamental understanding of blood clot breakage that underlies thrombotic embolization. STATEMENT OF SIGNIFICANCE: Fibrin, a naturally occurring biomaterial, is the major determinant of mechanical stability and integrity of blood clots and obstructive thrombi. We tested mechanically fibrin gels with single-edge cracks and followed ultrastructural alterations of the fibrin network. Rupture of fibrin gel involves initial alignment and elastic stretching of fibers followed by their eventual rupture for deformations reaching the critical level. To interpret the stress-strain curves, we developed Fluctuating Spring model, which showed that cracks render rupture of fibrin networks more spontaneous; yet, coupled fibrin fibers reinforce cracked fibrin networks. The results obtained provide fundamental understanding of blood clot breakage that underlies thrombotic embolization. Fluctuating Spring model can be applied to other protein networks with cracks and to interpret the stress-strain profiles.

Statistical Learning from Single-Molecule Experiments: Support Vector Machines and Expectation-Maximization Approaches to Understanding Protein Unfolding Data.

Single-molecule force spectroscopy has become a powerful tool for the exploration of dynamic processes that involve proteins; yet, meaningful interpretation of the experimental data remains challenging. Owing to low signal-to-noise ratio, experimental force-extension spectra contain force signals due to nonspecific interactions, tip or substrate detachment, and protein desorption. Unravelling of complex protein structures results in the unfolding transitions of different types. Here, we test the performance of Support Vector Machines (SVM) and Expectation Maximization (EM) approaches in statistical learning from dynamic force experiments. When the output from molecular modeling in silico (or other studies) is used as a training set, SVM and EM can be applied to understand the unfolding force data. The maximal margin or maximum likelihood classifier can be used to separate experimental test observations into the unfolding transitions of different types, and EM optimization can then be utilized to resolve the statistics of unfolding forces: weights, average forces, and standard deviations. We designed an EM-based approach, which can be directly applied to the experimental data without data classification and division into training and test observations. This approach performs well even when the sample size is small and when the unfolding transitions are characterized by overlapping force ranges.

Botulinum neurotoxin inhibitor binding dynamics and kinetics relevant for drug design.

BACKGROUND: A natural product analog, 3-(4-nitrophenyl)-7H-furo[3,2-g]chromen-7-one, which is a nitrophenyl psoralen (NPP) was found to be an effective inhibitor of botulinum neurotoxin type A (BoNT/A). METHODS: In this work, we performed enzyme inhibition kinetics and employed biochemical techniques such as isothermal calorimetry (ITC) and fluorescence spectroscopy as well as molecular modeling to examine the kinetics and binding mechanism of NPP inhibitor with BoNT/A LC. RESULTS: Studies of inhibition mechanism and binding dynamics of NPP to BoNT/A light chain (BoNT/A LC) showed that NPP is a mixed type inhibitor for the zinc endopeptidase activity, implying that at least part of the inhibitor-enzyme binding site may be different from the substrate-enzyme binding site. By using biochemical techniques, we demonstrated NPP forms a stable complex with BoNT/A LC. These observations were confirmed by Molecular Dynamics (MD) simulation, which demonstrates that NPP binds to the site near the active site. CONCLUSION: The NPP binding interferes with BoNT/A LC binding to the SNAP-25, hence, inhibits its cleavage. Based on these results, we propose a modified strategy for designing a molecule to enhance the efficiency of the inhibition against the neurotoxic effect of BoNT. GENERAL SIGNIFICANCE: Insights into the interactions of NPP with BoNT/A LC using biochemical and computational approaches will aid in the future development of effective countermeasures and better pharmacological strategies against botulism.

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.

Molecular packing structure of fibrin fibers resolved by X-ray scattering and molecular modeling.

Fibrin is the major extracellular component of blood clots and a proteinaceous hydrogel used as a versatile biomaterial. Fibrin forms branched networks built of laterally associated double-stranded protofibrils. This multiscale hierarchical structure is crucial for the extraordinary mechanical resilience of blood clots, yet the structural basis of clot mechanical properties remains largely unclear due, in part, to the unresolved molecular packing of fibrin fibers. Here the packing structure of fibrin fibers is quantitatively assessed by combining Small Angle X-ray Scattering (SAXS) measurements of fibrin reconstituted under a wide range of conditions with computational molecular modeling of fibrin protofibrils. The number, positions, and intensities of the Bragg peaks observed in the SAXS experiments were reproduced computationally based on the all-atom molecular structure of reconstructed fibrin protofibrils. Specifically, the model correctly predicts the intensities of the reflections of the 22.5 nm axial repeat, corresponding to the half-staggered longitudinal arrangement of fibrin molecules. In addition, the SAXS measurements showed that protofibrils within fibrin fibers have a partially ordered lateral arrangement with a characteristic transverse repeat distance of 13 nm, irrespective of the fiber thickness. These findings provide fundamental insights into the molecular structure of fibrin clots that underlies their biological and physical properties.

Botulinum Endopeptidase: SAXS Experiments and MD Simulations Reveal Extended Solution Structures That Account for Its Biochemical Properties.

Development of antidotes against botulism requires understanding of the enzymatically active conformations of Botulinum neurotoxin serotype A (BoNT/A) light chain (LCA). We performed small angle X-ray scattering (SAXS) to characterize the solution structures of truncated light chain (tLCA). The 34-37 Å radius of gyration of tLCA was 1.5-times greater than the averaged 22-23-Å radius from the crystal structures. The bimodal distribution of interatomic distances P(r) indicated the two-domain tLCA structure with 129-133 Å size, and Kratky plots indicated the tLCA partial unfolding in the 25-37 °C temperature range. To interpret these data, we employed molecular dynamics simulations and machine learning. Excellent agreement between experimental and theoretical P(r) profiles helped to resolve conformational subpopulations of tLCA in solution. Partial unfolding of the C-terminal portion of tLCA (residues 339-425) results in formation of extended conformations with the larger globular domain (residues 2-298) and the smaller unstructured domain (339-425). The catalytic domain, buried 20 Å-deep inside the crystal structure, becomes accessible in extended solution conformations (8-9 Å deep). The C- and N-termini containing different functional sequence motifs are maximally separated in the extended conformations. Our results offer physical insights into the molecular basis of BoNT/A function and stress the importance of reversible unfolding-refolding transitions and hydrophobic interactions.

Regulatory element in fibrin triggers tension-activated transition from catch to slip bonds.

Fibrin formation and mechanical stability are essential in thrombosis and hemostasis. To reveal how mechanical load impacts fibrin, we carried out optical trap-based single-molecule forced unbinding experiments. The strength of noncovalent A:a knob-hole bond stabilizing fibrin polymers first increases with tensile force (catch bonds) and then decreases with force when the force exceeds a critical value (slip bonds). To provide the structural basis of catch-slip-bond behavior, we analyzed crystal structures and performed molecular modeling of A:a knob-hole complex. The movable flap (residues γ295 to γ305) containing the weak calcium-binding site γ2 serves as a tension sensor. Flap dissociation from the B domain in the γ-nodule and translocation to knob 'A' triggers hole 'a' closure, resulting in the increase of binding affinity and prolonged bond lifetimes. The discovery of biphasic kinetics of knob-hole bond rupture is quantitatively explained by using a theory, formulated in terms of structural transitions in the binding pocket between the low-affinity (slip) and high-affinity (catch) states. We provide a general framework to understand the mechanical response of protein pairs capable of tension-induced remodeling of their association interface. Strengthening of the A:a knob-hole bonds at 30- to 40-pN forces might favor formation of nascent fibrin clots subject to hydrodynamic shear in vivo.

Atomic Structural Models of Fibrin Oligomers.

The space-filling fibrin network is a major part of clots and thrombi formed in blood. Fibrin polymerization starts when fibrinogen, a plasma protein, is proteolytically converted to fibrin, which self-assembles to form double-stranded protofibrils. When reaching a critical length, these intermediate species aggregate laterally to transform into fibers arranged into branched fibrin network. We combined multiscale modeling in silico with atomic force microscopy (AFM) imaging to reconstruct complete atomic models of double-stranded fibrin protofibrils with γ-γ crosslinking, A:a and B:b knob-hole bonds, and αC regions-all important structural determinants not resolved crystallographically. Structures of fibrin oligomers and protofibrils containing up to 19 monomers were successfully validated by quantitative comparison with high-resolution AFM images. We characterized the protofibril twisting, bending, kinking, and reversibility of A:a knob-hole bonds, and calculated hydrodynamic parameters of fibrin oligomers. Atomic structures of protofibrils provide a basis to understand mechanisms of early stages of fibrin polymerization.

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.

Dynamic Transition from α-Helices to ß-Sheets in Polypeptide Coiled-Coil Motifs.

We carried out dynamic force manipulations in silico on a variety of coiled-coil protein fragments from myosin, chemotaxis receptor, vimentin, fibrin, and phenylalanine zippers that vary in size and topology of their α-helical packing. When stretched along the superhelical axis, all superhelices show elastic, plastic, and inelastic elongation regimes and undergo a dynamic transition from the α-helices to the ß-sheets, which marks the onset of plastic deformation. Using the Abeyaratne-Knowles formulation of phase transitions, we developed a new theoretical methodology to model mechanical and kinetic properties of protein coiled-coils under mechanical nonequilibrium conditions and to map out their energy landscapes. The theory was successfully validated by comparing the simulated and theoretical force-strain spectra. We derived the scaling laws for the elastic force and the force for α-to-ß transition, which can be used to understand natural proteins' properties as well as to rationally design novel biomaterials of required mechanical strength with desired balance between stiffness and plasticity.